{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,12,7]],"date-time":"2024-12-07T05:21:06Z","timestamp":1733548866583,"version":"3.30.1"},"reference-count":146,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[1993,6,1]],"date-time":"1993-06-01T00:00:00Z","timestamp":738892800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":7351,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[1993,6]]},"DOI":"10.1016\/0012-365x(93)90393-8","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T03:43:34Z","timestamp":1027655014000},"page":"17-54","source":"Crossref","is-referenced-by-count":3,"title":["The family of block designs with some combinatorial properties"],"prefix":"10.1016","volume":"116","author":[{"given":"Sanpei","family":"Kageyama","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0012-365X(93)90393-8_BIB1","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1080\/01621459.1963.10500832","article-title":"Techniques for constructing fractional replicate plans","volume":"58","author":"Addelman","year":"1963","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/0012-365X(93)90393-8_BIB2","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1177\/0008068319650107","article-title":"A note on incomplete block designs","volume":"14","author":"Agrawal","year":"1965","journal-title":"Calcutta Statist. Assoc. Bull."},{"key":"10.1016\/0012-365X(93)90393-8_BIB3","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1002\/bimj.4710220105","article-title":"A necessary condition for balance of a block design","volume":"22","author":"Baksalary","year":"1980","journal-title":"Biometrical J."},{"key":"10.1016\/0012-365X(93)90393-8_BIB4","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0378-3758(88)90022-5","article-title":"Criteria for the validity of Fisher's condition for balanced block designs","volume":"18","author":"Baksalary","year":"1988","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB5","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0378-3758(85)90077-1","article-title":"Existence and constructions of connected block designs with given vectors of treatment replications and block sizes","volume":"12","author":"Baksalary","year":"1985","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB6","doi-asserted-by":"crossref","first-page":"147","DOI":"10.2307\/3315203","article-title":"Connectedness of PBIB designs","volume":"15","author":"Baksalary","year":"1987","journal-title":"Canad. J. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB7","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1093\/qmath\/28.4.433","article-title":"On tight designs","volume":"28","author":"Bannai","year":"1977","journal-title":"Quart. J. Math. Oxford"},{"journal-title":"personal communication","year":"1979","author":"Bannai","key":"10.1016\/0012-365X(93)90393-8_BIB8"},{"year":"1985","series-title":"Design Theory","author":"Beth","key":"10.1016\/0012-365X(93)90393-8_BIB9"},{"key":"10.1016\/0012-365X(93)90393-8_BIB10","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF01930873","article-title":"On the parameters of strongly resolvable designs","volume":"19","author":"Beutelspacher","year":"1982","journal-title":"J. Geom."},{"key":"10.1016\/0012-365X(93)90393-8_BIB11","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF01788072","article-title":"Symmetry and classification of certain regular group divisible designs","volume":"2","author":"Bhagwandas","year":"1986","journal-title":"Graphs Combin."},{"key":"10.1016\/0012-365X(93)90393-8_BIB12","first-page":"105","article-title":"A note on the resolvability of balanced incomplete block designs","volume":"6","author":"Bose","year":"1942","journal-title":"Sankhy\u0101"},{"key":"10.1016\/0012-365X(93)90393-8_BIB13","first-page":"249","article-title":"On a resolvable series of balanced incomplete block designs","volume":"8","author":"Bose","year":"1947","journal-title":"Sankhy\u0101"},{"year":"1950","series-title":"Least square aspects of analysis of variance","author":"Bose","key":"10.1016\/0012-365X(93)90393-8_BIB14"},{"key":"10.1016\/0012-365X(93)90393-8_BIB15","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1214\/aoms\/1177729382","article-title":"Combinatorial properties of group divisible incomplete block designs","volume":"23","author":"Bose","year":"1952","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB16","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1080\/01621459.1952.10501161","article-title":"Classification and analysis of partially balanced incomplete block designs with two associate classes","volume":"47","author":"Bose","year":"1952","journal-title":"J. Amer. Statist. Assoc."},{"key":"10.1016\/0012-365X(93)90393-8_BIB17","doi-asserted-by":"crossref","first-page":"177","DOI":"10.4153\/CJM-1960-015-8","article-title":"On the composition of balanced incomplete block designs","volume":"12","author":"Bose","year":"1960","journal-title":"Canad. J. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB18","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1214\/aoms\/1177729027","article-title":"On the construction of group divisible incomplete block designs","volume":"24","author":"Bose","year":"1953","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB19","first-page":"353","article-title":"A diophantine equation arising from tight 4-designs","volume":"16","author":"Bremner","year":"1979","journal-title":"Osaka J. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB20","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/0097-3165(88)90049-0","article-title":"An application of Ryser's (x, y)-theorem to a problem in statistics","volume":"47","author":"Bridges","year":"1988","journal-title":"J. Combin. Theory Ser. A"},{"key":"10.1016\/0012-365X(93)90393-8_BIB21","doi-asserted-by":"crossref","first-page":"275","DOI":"10.2307\/2528995","article-title":"On some desirable patterns in block designs (with discussion)","volume":"27","author":"Cali\u0144ski","year":"1971","journal-title":"Biometrics"},{"key":"10.1016\/0012-365X(93)90393-8_BIB22","series-title":"Recent Developments in Statistics","first-page":"365","article-title":"On the notion of balance in block designs","author":"Cali\u0144ski","year":"1977"},{"key":"10.1016\/0012-365X(93)90393-8_BIB23","first-page":"299","article-title":"Supplemented block designs","volume":"16","author":"Cali\u0144ski","year":"1974","journal-title":"Biometrical J."},{"key":"10.1016\/0012-365X(93)90393-8_BIB24","series-title":"Mathematical Statistics and Probability Theory","first-page":"47","article-title":"On the notion of efficiency of a block design","author":"Cali\u0144ski","year":"1980"},{"year":"1956","series-title":"Introduction to the Theory of Groups of Finite Order","author":"Carmichael","key":"10.1016\/0012-365X(93)90393-8_BIB25"},{"key":"10.1016\/0012-365X(93)90393-8_BIB26","first-page":"39","article-title":"Tight (2t + 1)-designs","volume":"14","author":"Carmony","year":"1978","journal-title":"Utilitas Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB27","first-page":"199","article-title":"A new class of C-designs","volume":"48","author":"Ceranka","year":"1986","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB28","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0378-3758(78)90025-3","article-title":"On some properties of the dual of a totally balanced block design","volume":"2","author":"Ceranka","year":"1978","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB29","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0378-3758(86)90123-0","article-title":"A note on the inequality b\u2a7et for block designs","volume":"13","author":"Ceranka","year":"1986","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB30","first-page":"580","article-title":"Graph and optimum design theories \u2013 some connections and examples","volume":"49","author":"Cheng","year":"1981","journal-title":"Bull. Int. Statist. Inst."},{"key":"10.1016\/0012-365X(93)90393-8_BIB31","article-title":"Tables of Two-Associate-Class Partially Balanced Designs","volume":"63","author":"Clatworthy","year":"1973"},{"volume":"Vol. 34","article-title":"Combinatorial Design Theory","year":"1987","key":"10.1016\/0012-365X(93)90393-8_BIB32"},{"key":"10.1016\/0012-365X(93)90393-8_BIB33","series-title":"IMA preprint series #400","article-title":"Applications of combinatorial designs in computer science","author":"Colbourn","year":"1988"},{"key":"10.1016\/0012-365X(93)90393-8_BIB34","doi-asserted-by":"crossref","first-page":"499","DOI":"10.2307\/2527896","article-title":"Balanced block designs with two different numbers of replicates","volume":"18","author":"Corsten","year":"1962","journal-title":"Biometrics"},{"key":"10.1016\/0012-365X(93)90393-8_BIB35","first-page":"67","article-title":"Balancing incomplete block designs","volume":"47","author":"Das","year":"1985","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB36","first-page":"461","article-title":"A note on balanced designs","volume":"37","author":"Dey","year":"1975","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB37","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/BF02479813","article-title":"An inequality for tactical configurations","volume":"26","author":"Dey","year":"1974","journal-title":"Ann. Inst. Statist. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB38","first-page":"33","article-title":"Bibliography of Kirkman's school girl problem","volume":"41\u201342","author":"Eckenstein","year":"1912","journal-title":"Messenger of Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB39","first-page":"39","article-title":"Tight 4-designs","volume":"16","author":"Enomoto","year":"1979","journal-title":"Osaka J. Math."},{"year":"1925","series-title":"Statistical Methods for Research Workers","author":"Fisher","key":"10.1016\/0012-365X(93)90393-8_BIB40"},{"key":"10.1016\/0012-365X(93)90393-8_BIB41","first-page":"503","article-title":"The arrangement of field experiments","volume":"33","author":"Fisher","year":"1926","journal-title":"J. Ministry Agriculture"},{"year":"1938-1963","series-title":"Statistical Tables for Biological, Agricultural and Medical Research","author":"Fisher","key":"10.1016\/0012-365X(93)90393-8_BIB42"},{"key":"10.1016\/0012-365X(93)90393-8_BIB43","first-page":"204","article-title":"On robustness of designs against incomplete data","volume":"40","author":"Ghosh","year":"1979","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB44","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01418308","article-title":"Intersection triangles and block intersection numbers of Steiner systems","volume":"139","author":"Gross","year":"1974","journal-title":"Math. Z."},{"key":"10.1016\/0012-365X(93)90393-8_BIB45","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1177\/0008068319870110","article-title":"A note on the notion of balance in designs","volume":"36","author":"Gupta","year":"1987","journal-title":"Calcutta Statist. Assoc. Bull."},{"journal-title":"A characterization of binary completely symmetric connected block designs with v=b based on n\u22610(modv) experimental units","year":"1981","author":"Hedayat","key":"10.1016\/0012-365X(93)90393-8_BIB46"},{"key":"10.1016\/0012-365X(93)90393-8_BIB47","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1214\/aos\/1176342620","article-title":"Resistant and susceptible BIB designs","volume":"2","author":"Hedayat","year":"1974","journal-title":"Ann. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB48","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0378-3758(80)90006-3","article-title":"The family of t-designs \u2013 Part I","volume":"4","author":"Hedayat","year":"1980","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB49","doi-asserted-by":"crossref","first-page":"761","DOI":"10.2307\/2373244","article-title":"On t-designs and groups","volume":"87","author":"Hughes","year":"1965","journal-title":"Amer. J. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB50","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF00148147","article-title":"On resolutions and Bose's theorem","volume":"5","author":"Hughes","year":"1976","journal-title":"Geom. Dedicata"},{"year":"1985","series-title":"Design Theory","author":"Hughes","key":"10.1016\/0012-365X(93)90393-8_BIB51"},{"key":"10.1016\/0012-365X(93)90393-8_BIB52","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1007\/BF01832859","article-title":"Inequalities for t-designs with repeated blocks","volume":"10","author":"Ho","year":"1974","journal-title":"Aequationes Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB53","first-page":"493","article-title":"On tight 4-designs","volume":"12","author":"Ito","year":"1975","journal-title":"Osaka J. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB54","first-page":"693","article-title":"Corrections and supplements to \u2018On tight 4-designs\u2019","volume":"15","author":"Ito","year":"1978","journal-title":"Osaka J. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB55","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1080\/00401706.1961.10489926","article-title":"An application of a balanced incomplete block design","volume":"3","author":"John","year":"1961","journal-title":"Technometrics"},{"key":"10.1016\/0012-365X(93)90393-8_BIB56","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1111\/j.2517-6161.1959.tb00326.x","article-title":"On a property of incomplete blocks","volume":"21","author":"Jones","year":"1959","journal-title":"J. Roy. Statist. Soc. B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB57","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1214\/aoms\/1177693259","article-title":"An improved inequality for balanced incomplete block designs","volume":"42","author":"Kageyama","year":"1971","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB58","doi-asserted-by":"crossref","first-page":"269","DOI":"10.2307\/1402466","article-title":"A survey of resolvable solutions of balanced incomplete block designs","volume":"40","author":"Kageyama","year":"1972","journal-title":"Internat. Statist. Rev."},{"key":"10.1016\/0012-365X(93)90393-8_BIB59","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1214\/aos\/1193342400","article-title":"On \u03bc-resolvable and affine \u03bc-resolvable balanced incomplete block designs","volume":"1","author":"Kageyama","year":"1973","journal-title":"Ann. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB60","doi-asserted-by":"crossref","first-page":"527","DOI":"10.32917\/hmj\/1206136840","article-title":"Reduction of associate classes for block designs and related combinatorial arrangements","volume":"4","author":"Kageyama","year":"1974","journal-title":"Hiroshima Math. J."},{"key":"10.1016\/0012-365X(93)90393-8_BIB61","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1007\/BF02504671","article-title":"Note on an inequality for tactical configurations","volume":"27","author":"Kageyama","year":"1975","journal-title":"Ann. Inst. Statist. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB62","series-title":"Essays in Probability and Statistics","article-title":"On \u03bc-resolvable and affine \u03bc-resolvable t-designs","author":"Kageyama","year":"1976"},{"key":"10.1016\/0012-365X(93)90393-8_BIB63","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1214\/aos\/1176343475","article-title":"Resolvability of block designs","volume":"4","author":"Kageyama","year":"1976","journal-title":"Ann. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB64","first-page":"19","article-title":"Conditions for \u03b1-resolvability and affine \u03b1-resolvability of incomplete block designs","volume":"7","author":"Kageyama","year":"1977","journal-title":"J. Japan Statist. Soc."},{"issue":"5","key":"10.1016\/0012-365X(93)90393-8_BIB65","first-page":"312","article-title":"Remarks on \u2018Resolvability of block designs\u2019","volume":"7","author":"Kageyama","year":"1978","journal-title":"Bull. Inst. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB66","first-page":"65","article-title":"Relation between experimental designs and matrix theory: Applications","volume":"2","author":"Kageyama","year":"1979"},{"key":"10.1016\/0012-365X(93)90393-8_BIB67","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1080\/03610928008827905","article-title":"On properties of efficiency-balanced designs","volume":"9","author":"Kageyama","year":"1980","journal-title":"Comm. Statist. Theory Methods"},{"key":"10.1016\/0012-365X(93)90393-8_BIB68","first-page":"171","article-title":"On 5-designs","volume":"19","author":"Kageyama","year":"1981","journal-title":"Utilitas Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB69","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0378-3758(82)90020-9","article-title":"Connectedness of two-associate PBIB designs","volume":"7","author":"Kageyama","year":"1982","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB70","series-title":"Enumeration and Design","article-title":"On variance-balanced block designs with b = v","author":"Kageyama","year":"1984"},{"key":"10.1016\/0012-365X(93)90393-8_BIB71","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/BF00147652","article-title":"Some properties on resolvability of variance-balanced designs","volume":"15","author":"Kageyama","year":"1984","journal-title":"Geom. Dedicata"},{"key":"10.1016\/0012-365X(93)90393-8_BIB72","series-title":"Linear Statistical Inference","first-page":"99","article-title":"Connected designs with the minimum number of experimental units","volume":"Vol. 35","author":"Kageyama","year":"1985"},{"key":"10.1016\/0012-365X(93)90393-8_BIB73","first-page":"195","article-title":"Two methods of construction of affine resolvable balanced designs with unequal block sizes","volume":"50","author":"Kageyama","year":"1988","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB74","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/0378-3758(83)90019-8","article-title":"The family of t-designs \u2014 Part II","volume":"7","author":"Kageyama","year":"1983","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB75","first-page":"47","article-title":"On non-existence of symmetrical variance-balanced designs","volume":"11","author":"Kageyama","year":"1988"},{"key":"10.1016\/0012-365X(93)90393-8_BIB76","first-page":"137","article-title":"Parametric characterizations of BIB designs","volume":"8","author":"Kageyama","year":"1985"},{"key":"10.1016\/0012-365X(93)90393-8_BIB77_1","first-page":"380","article-title":"General balanced designs through reinforcement","volume":"48","author":"Kageyama","year":"1986","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB77_2","first-page":"103","article-title":"Addendum","volume":"49","author":"Kageyama","year":"1987","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB78","first-page":"225","article-title":"Non-existence of tight (2s+1)-designs","volume":"17","author":"Kageyama","year":"1980","journal-title":"Utilitas Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB79","series-title":"Recent Developments in Statistical Inference and Data Analysis","first-page":"171","article-title":"Non-existence of equireplicated variance-balanced designs with b = v + 1","author":"Kageyama","year":"1980"},{"key":"10.1016\/0012-365X(93)90393-8_BIB80","first-page":"137","article-title":"Some constructions of balanced bipartite block designs","volume":"33","author":"Kageyama","year":"1988","journal-title":"Utilitas Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB81","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0378-3758(77)90020-9","article-title":"Characterization of certain incomplete block designs","volume":"1","author":"Kageyama","year":"1977","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB82","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0378-3758(79)90002-8","article-title":"Inequality for equireplicated n-ary block designs with unequal block sizes","volume":"3","author":"Kageyama","year":"1979","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB83","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0378-3758(80)90004-X","article-title":"Some bounds on balanced block designs","volume":"4","author":"Kageyama","year":"1980","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB84","first-page":"85","article-title":"A condition for the validity of Fisher's inequality","volume":"14","author":"Kageyama","year":"1984","journal-title":"J. Japan Statist. Soc."},{"key":"10.1016\/0012-365X(93)90393-8_BIB85","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1080\/03610928808829705","article-title":"D-1-partially efficiency-balanced designs with at most two efficiency classes","volume":"17","author":"Kageyama","year":"1988","journal-title":"Comm. Statist. Theory Methods"},{"key":"10.1016\/0012-365X(93)90393-8_BIB86","doi-asserted-by":"crossref","first-page":"1398","DOI":"10.1214\/aoms\/1177699284","article-title":"On the block structure of singular group divisible designs","volume":"37","author":"Kapadia","year":"1966","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB87","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF01110942","article-title":"On the construction of certain Hadamard designs","volume":"119","author":"Kimberley","year":"1971","journal-title":"Math. Z."},{"key":"10.1016\/0012-365X(93)90393-8_BIB88","first-page":"191","article-title":"On a problem in combinatorics","volume":"2","author":"Kirkman","year":"1847","journal-title":"Cambridge Dublin Math. J."},{"key":"10.1016\/0012-365X(93)90393-8_BIB89","first-page":"48","article-title":"Query","author":"Kirkman","year":"1850","journal-title":"Ladies and Gentleman's Diary"},{"key":"10.1016\/0012-365X(93)90393-8_BIB90","first-page":"191","article-title":"Note on an unanswered prize question","volume":"5","author":"Kirkman","year":"1850","journal-title":"Cambridge Dublin Math. J."},{"key":"10.1016\/0012-365X(93)90393-8_BIB91","first-page":"329","article-title":"Symmetrical unequal block arrangements","volume":"5","author":"Kishen","year":"1940","journal-title":"Sankhy\u0101"},{"key":"10.1016\/0012-365X(93)90393-8_BIB92","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0012-365X(78)90179-6","article-title":"A note on partial parallel classes in Steiner systems","volume":"24","author":"Lindner","year":"1978","journal-title":"Discrete Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB93","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0012-365X(78)90122-X","article-title":"Steiner quadruple systems \u2013 a survey","volume":"22","author":"Lindner","year":"1978","journal-title":"Discrete Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB94","article-title":"Topics on Steiner systems","volume":"Vol. 7","author":"Lindner","year":"1980"},{"key":"10.1016\/0012-365X(93)90393-8_BIB95","first-page":"195","article-title":"Simple six designs exist","volume":"40","author":"Magliveras","year":"1983","journal-title":"Congr. Numer."},{"key":"10.1016\/0012-365X(93)90393-8_BIB96","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1214\/aoms\/1177704485","article-title":"On the parameters and intersection of blocks of balanced incomplete block designs","volume":"33","author":"Majindar","year":"1962","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB97","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1214\/aoms\/1177697740","article-title":"A note on balanced incomplete block designs","volume":"40","author":"Mann","year":"1969","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB98","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1007\/BF01110993","article-title":"On the structure of affine designs","volume":"125","author":"Mavron","year":"1972","journal-title":"Math. Z."},{"key":"10.1016\/0012-365X(93)90393-8_BIB99","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1214\/aoms\/1177705921","article-title":"An inequality for balanced incomplete block designs","volume":"31","author":"Mikhail","year":"1960","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB100","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0378-3758(81)90030-6","article-title":"A criterion for connectedness in two-associate class PBIB designs","volume":"5","author":"Mohan","year":"1981","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/0012-365X(93)90393-8_BIB101","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1093\/biomet\/72.1.165","article-title":"On resolvable and affine resolvable variance-balanced designs","volume":"72","author":"Mukerjee","year":"1985","journal-title":"Biometrika"},{"key":"10.1016\/0012-365X(93)90393-8_BIB102","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/BF01230331","article-title":"An inequality for strongly resolvable designs","volume":"27","author":"Mukerjee","year":"1986","journal-title":"J. Geom."},{"key":"10.1016\/0012-365X(93)90393-8_BIB103","first-page":"51","article-title":"Classification of semi-regular group divisible designs","volume":"25","author":"Mukerjee","year":"1988","journal-title":"Ars Combin."},{"key":"10.1016\/0012-365X(93)90393-8_BIB104","first-page":"615","article-title":"Incomplete block designs for experiments involving several groups of varieties","volume":"7","author":"Nair","year":"1942","journal-title":"Science and Culture"},{"year":"1974","series-title":"Statistical Theory of the Analysis of Experimental Designs","author":"Ogawa","key":"10.1016\/0012-365X(93)90393-8_BIB105"},{"key":"10.1016\/0012-365X(93)90393-8_BIB106","series-title":"Combinatorics and Applications","first-page":"248","article-title":"Connectedness of PBIB designs with applications","author":"Ogawa","year":"1984"},{"key":"10.1016\/0012-365X(93)90393-8_BIB107","doi-asserted-by":"crossref","first-page":"353","DOI":"10.2307\/2982222","article-title":"The use and classification of non-orthogonal designs","volume":"126","author":"Pearce","year":"1963","journal-title":"J. Roy. Statist. Soc. A"},{"key":"10.1016\/0012-365X(93)90393-8_BIB108","doi-asserted-by":"crossref","first-page":"699","DOI":"10.2307\/2528123","article-title":"Experimenting with blocks of natural sizes","volume":"20","author":"Pearce","year":"1964","journal-title":"Biometrika"},{"key":"10.1016\/0012-365X(93)90393-8_BIB109","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1093\/biomet\/57.2.339","article-title":"The efficiency of block designs in general","volume":"57","author":"Pearce","year":"1970","journal-title":"Biometrika"},{"key":"10.1016\/0012-365X(93)90393-8_BIB110","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1093\/biomet\/61.3.449","article-title":"The basic contrasts of an experimental design with special reference to the analysis of data","volume":"61","author":"Pearce","year":"1974","journal-title":"Biometrika"},{"key":"10.1016\/0012-365X(93)90393-8_BIB111","first-page":"417","article-title":"On tight 6-designs","volume":"14","author":"Peterson","year":"1977","journal-title":"Osaka J. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB112","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1080\/03610928508828978","article-title":"Constructions of partially efficiency-balanced designs and their analysis","volume":"14","author":"Puri","year":"1985","journal-title":"Comm. Statist. Theory Methods"},{"key":"10.1016\/0012-365X(93)90393-8_BIB113","first-page":"457","article-title":"A note on efficiency balanced designs","volume":"37","author":"Puri","year":"1975","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB114","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1080\/03610927708827527","article-title":"Partially efficiency balanced designs","volume":"6","author":"Puri","year":"1977","journal-title":"Comm. Statist. Theory Methods"},{"key":"10.1016\/0012-365X(93)90393-8_BIB115","first-page":"189","article-title":"Supplemented designs","volume":"39","author":"Puri","year":"1977","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB116","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1214\/aoms\/1177705806","article-title":"On the block structure of certain PBIB designs with triangular and L2 association schemes","volume":"31","author":"Raghavarao","year":"1960","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB117","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1093\/biomet\/49.3-4.561","article-title":"On balanced unequal block designs","volume":"49","author":"Raghavarao","year":"1962","journal-title":"Biometrika"},{"key":"10.1016\/0012-365X(93)90393-8_BIB118","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1214\/aoms\/1177704586","article-title":"Symmetrical unequal block arrangements with two unequal block sizes","volume":"33","author":"Raghavarao","year":"1962","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB119","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/BF02506369","article-title":"Some results on tactical configurations and non-existence of difference set solutions for certain symmetrical PBIB designs","volume":"22","author":"Raghavarao","year":"1970","journal-title":"Ann. Inst. Statist. Math."},{"year":"1971","series-title":"Constructions and Combinatorial Problems in Design of Experiments","author":"Raghavarao","key":"10.1016\/0012-365X(93)90393-8_BIB120"},{"key":"10.1016\/0012-365X(93)90393-8_BIB121","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1177\/0008068319660106","article-title":"A note on equi-replicated balanced designs with b=v","volume":"15","author":"Rao","year":"1966","journal-title":"Calcutta Statist. Assoc. Bull."},{"key":"10.1016\/0012-365X(93)90393-8_BIB122","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1214\/aoms\/1177706729","article-title":"A note on balanced designs","volume":"29","author":"Rao","year":"1958","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB123","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1090\/pspum\/019\/9959","article-title":"Solution of Kirkman's school girl problem","volume":"19","author":"Ray-Chaudhuri","year":"1971","journal-title":"Combinatorics, Amer. Math. Soc."},{"key":"10.1016\/0012-365X(93)90393-8_BIB124","first-page":"734","article-title":"On t-designs","volume":"12","author":"Ray-Chaudhuri","year":"1975","journal-title":"Osaka J. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB125","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1214\/aoms\/1177706977","article-title":"On partially balanced linked block designs","volume":"28","author":"Roy","year":"1957","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB126","first-page":"383","article-title":"On Calinski's patterns in block designs","volume":"38","author":"Saha","year":"1976","journal-title":"Sankhy\u0101 B"},{"key":"10.1016\/0012-365X(93)90393-8_BIB127","first-page":"169","article-title":"On connectedness-conditions of PBIB designs","volume":"14","author":"Saha","year":"1984","journal-title":"J. Japan Statist. Soc."},{"key":"10.1016\/0012-365X(93)90393-8_BIB128","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1214\/aoms\/1177703763","article-title":"An upper bound for the number of disjoint blocks in certain PBIB designs","volume":"35","author":"Shah","year":"1964","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB129","first-page":"13","article-title":"A note on the block structure of incomplete block designs","volume":"5","author":"Shah","year":"1967","journal-title":"J. Indian Statist. Assoc."},{"key":"10.1016\/0012-365X(93)90393-8_BIB130","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/BF01835977","article-title":"Affine resolvable balanced incomplete block designs: a survey","volume":"14","author":"Shrikhande","year":"1976","journal-title":"Aequationes Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB131","series-title":"Contributions to Statistics","first-page":"471","article-title":"Affine \u03b1-resolvable incomplete block designs","author":"Shrikhande","year":"1964"},{"key":"10.1016\/0012-365X(93)90393-8_BIB132","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1214\/aoms\/1177728433","article-title":"Balanced incomplete block designs and tactical configurations","volume":"26","author":"Sprott","year":"1955","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB133","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1214\/aoms\/1177706814","article-title":"A note on BIBDs","volume":"28","author":"Stanton","year":"1957","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB134","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1214\/aoms\/1177699279","article-title":"Inductive methods for balanced incomplete block designs","volume":"37","author":"Stanton","year":"1966","journal-title":"Ann. Math. Statist."},{"key":"10.1016\/0012-365X(93)90393-8_BIB135","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1515\/crll.1853.45.181","article-title":"Combinatorische Aufgabe","volume":"45","author":"Steiner","year":"1853","journal-title":"J. Reine Angew. Math."},{"year":"1987","series-title":"Combinatorics of Experimental Design","author":"Street","key":"10.1016\/0012-365X(93)90393-8_BIB136"},{"key":"10.1016\/0012-365X(93)90393-8_BIB137","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0012-365X(87)90061-6","article-title":"Nontrivial t-designs without repeated blocks exist for all t","volume":"65","author":"Teirlinck","year":"1987","journal-title":"Discrete Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB138","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1111\/j.2517-6161.1952.tb00101.x","article-title":"The design and analysis of block experiments (with discussion)","volume":"14","author":"Tocher","year":"1952","journal-title":"J. Roy. Statist. Soc. B"},{"year":"1988","series-title":"Combinatorial Designs","author":"Wallis","key":"10.1016\/0012-365X(93)90393-8_BIB139"},{"key":"10.1016\/0012-365X(93)90393-8_BIB140","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0097-3165(83)90065-1","article-title":"Inequalities for t designs","volume":"34","author":"Wilson","year":"1983","journal-title":"J. Combin. Theory Ser. A"},{"key":"10.1016\/0012-365X(93)90393-8_BIB141","first-page":"805","article-title":"Generalization of Fisher's inequality to t-designs","volume":"18","author":"Wilson","year":"1971","journal-title":"Notices Amer. Math. Soc."},{"key":"10.1016\/0012-365X(93)90393-8_BIB142","article-title":"Prize question 1733","author":"Woolhouse","year":"1844","journal-title":"Ladies and Gentleman's Diary"},{"key":"10.1016\/0012-365X(93)90393-8_BIB143","first-page":"357","article-title":"Two-way classification designs with unequal cell frequencies","volume":"32","author":"Yamamoto","year":"1968"},{"key":"10.1016\/0012-365X(93)90393-8_BIB144","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/BF02504632","article-title":"Balanced arrays of strength 2l and balanced fractional 2m factorial designs","volume":"27","author":"Yamamoto","year":"1975","journal-title":"Ann. Inst. Statist. Math."},{"key":"10.1016\/0012-365X(93)90393-8_BIB145","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1111\/j.1469-1809.1936.tb02134.x","article-title":"Incomplete randomized blocks","volume":"7","author":"Yates","year":"1936","journal-title":"Ann. Eugen. Lond."}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0012365X93903938?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0012365X93903938?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T21:49:29Z","timestamp":1733521769000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0012365X93903938"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,6]]},"references-count":146,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1993,6]]}},"alternative-id":["0012365X93903938"],"URL":"https:\/\/doi.org\/10.1016\/0012-365x(93)90393-8","relation":{},"ISSN":["0012-365X"],"issn-type":[{"type":"print","value":"0012-365X"}],"subject":[],"published":{"date-parts":[[1993,6]]}}}