{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T23:20:12Z","timestamp":1697671212082},"reference-count":35,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[2003,5,1]],"date-time":"2003-05-01T00:00:00Z","timestamp":1051747200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3766,"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":[[2003,5]]},"DOI":"10.1016\/s0012-365x(02)00795-1","type":"journal-article","created":{"date-parts":[[2003,5,19]],"date-time":"2003-05-19T16:52:26Z","timestamp":1053363146000},"page":"3-36","source":"Crossref","is-referenced-by-count":2,"title":["Existence of OBIBDs with k=4 with and without nesting"],"prefix":"10.1016","volume":"266","author":[{"given":"R.Julian R.","family":"Abel","sequence":"first","affiliation":[]},{"given":"Malcolm","family":"Greig","sequence":"additional","affiliation":[]},{"given":"D.H.","family":"Rees","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0012-365X(02)00795-1_BIB1","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0378-3758(99)00114-7","article-title":"Perfect Mendelsohn designs with block size six","volume":"86","author":"Abel","year":"2000","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB2","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1002\/jcd.1010","article-title":"Balance incomplete block designs with block size 8","volume":"9","author":"Abel","year":"2001","journal-title":"J. Combin. Des."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB3","series-title":"C.R.C. Handbook of Combinatorial Designs","first-page":"111","article-title":"Mutually orthogonal Latin squares (MOLS)","author":"Abel","year":"1996"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB4","series-title":"C.R.C. Handbook of Combinatorial Designs","first-page":"142","article-title":"Incomplete MOLS","author":"Abel","year":"1996"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB5","first-page":"175","article-title":"Pitch tournament designs and other BIBDs\u2014existence results for the case v=8n+1","volume":"138","author":"Abel","year":"1999","journal-title":"Congr. Numer."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB6","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1002\/jcd.1015","article-title":"Pitch tournament designs and other BIBDs\u2014existence results for the case v=8n","volume":"9","author":"Abel","year":"2001","journal-title":"J. Combin. Des."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB7","series-title":"C.R.C. Handbook of Combinatorial Designs","first-page":"41","article-title":"BIBDs with small block size","author":"Abel","year":"1996"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0012-365X(00)00123-0","article-title":"Resolvable BIBDs block size 7 and index 6","volume":"226","author":"Abel","year":"2001","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB9","series-title":"Combinatorial Designs and Tournaments","author":"Anderson","year":"1997"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB10","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/S0195-6698(80)80019-9","article-title":"A series of separable designs with application to pairwise orthogonal Latin squares","volume":"1","author":"Brouwer","year":"1990","journal-title":"European J. Combin."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB11","doi-asserted-by":"crossref","unstructured":"M. Buratti, Difference families and Frobenius groups, preprint, 2000.","DOI":"10.1006\/jcta.1999.3038"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB12","series-title":"Combinatorics Advances","first-page":"27","article-title":"Construction techniques for mutually orthogonal Latin squares","author":"Colbourn","year":"1995"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB13","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1093\/biomet\/62.2.341","article-title":"Connectedness and orthogonality in multi-factor designs","volume":"62","author":"Eccleston","year":"1975","journal-title":"Biometrika"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB14","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1093\/biomet\/64.2.339","article-title":"Adjusted orthogonality in nonorthogonal designs","volume":"64","author":"Eccleston","year":"1977","journal-title":"Biometrika"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB15","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0012-365X(91)90433-3","article-title":"Difference families from rings","volume":"97","author":"Furino","year":"1991","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB16","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1002\/(SICI)1520-6610(1999)7:5<341::AID-JCD5>3.0.CO;2-1","article-title":"Designs from projective planes, and PBD bases","volume":"7","author":"Greig","year":"1999","journal-title":"J. Combin. Des."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB17","first-page":"3","article-title":"Recursive constructions of balanced incomplete block designs with block size of 7, 8, or 9","volume":"60","author":"Greig","year":"2001","journal-title":"Ars Combin."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB18","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1023\/A:1008224620163","article-title":"Resolvable balanced incomplete block designs with a block size of 8","volume":"11","author":"Greig","year":"1997","journal-title":"Des. Codes Cryptogr."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB19","doi-asserted-by":"crossref","unstructured":"M. Greig, D.H. Rees, Existence of balanced incomplete block designs for many sets of treatments, Discrete Math. 261 (2003) 299\u2013324.","DOI":"10.1016\/S0012-365X(02)00476-4"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB20","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1006\/jcta.1997.2742","article-title":"Pairwise balanced designs with block sizes 8, 9 and 10","volume":"77","author":"Ling","year":"1997","journal-title":"J. Combin. Theory Ser. A"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB21","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/S0378-3758(99)00127-5","article-title":"V(m,t)'s for m=4,5,6","volume":"86","author":"Ling","year":"2000","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB22","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0378-3758(98)00056-1","article-title":"Properties of superimposed BIBDs","volume":"73","author":"Morgan","year":"1998","journal-title":"J. Statist. Plann. Inference"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB23","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0012-365X(00)00332-0","article-title":"Nested balanced incomplete block designs","volume":"231","author":"Morgan","year":"2001","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB24","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1214\/aos\/1032526963","article-title":"Optimal blocked main effects plans with nested rows and columns and related designs","volume":"24","author":"Morgan","year":"1996","journal-title":"Ann. Statist."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB25_1","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1093\/biomet\/53.3-4.497","article-title":"Some balanced incomplete block designs for two sets of treatments","volume":"53","author":"Preece","year":"1966","journal-title":"Biometrika"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB25_2","first-page":"691","article-title":"Corrigendum","volume":"56","author":"Preece","year":"1969","journal-title":"Biometrika"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB26","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1093\/biomet\/54.3-4.479","article-title":"Nested balanced incomplete block designs","volume":"54","author":"Preece","year":"1967","journal-title":"Biometrika"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB27","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1111\/j.1467-842X.1996.tb00678.x","article-title":"Multi-factor balanced block designs with complete adjusted orthogonality for all pairs of treatment factors","volume":"38","author":"Preece","year":"1996","journal-title":"Austral. J. Statist."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB28","first-page":"159","article-title":"A generalisation of some Kirkman designs","volume":"32","author":"Rees","year":"1987","journal-title":"Utilitas Math."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB29","first-page":"177","article-title":"Some new generalized Kirkman systems","volume":"56","author":"Rees","year":"1999","journal-title":"Utilitas Math."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB30","unstructured":"D.H. Rees, Nested pergolas, preprint."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB31","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1016\/S0012-365X(99)90135-8","article-title":"Perfect Graeco-Latin balanced incomplete block designs (pergolas)","volume":"197\/198","author":"Rees","year":"1999","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB32","doi-asserted-by":"crossref","unstructured":"D.J. Street, Graeco-Latin and Nested Row and Column Designs, Lecture Notes in Mathematics, Vol. 884, Springer, Berlin, 1981, pp. 304\u2013313.","DOI":"10.1007\/BFb0091827"},{"key":"10.1016\/S0012-365X(02)00795-1_BIB33","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1002\/(SICI)1520-6610(2000)8:3<218::AID-JCD7>3.0.CO;2-8","article-title":"Three new constructions of mutually orthogonal Latin squares","volume":"8","author":"Wojtas","year":"2000","journal-title":"J. Combin. Des."},{"key":"10.1016\/S0012-365X(02)00795-1_BIB34","unstructured":"M. Wojtas, Personal communication."}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X02007951?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X02007951?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,17]],"date-time":"2020-03-17T16:57:05Z","timestamp":1584464225000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0012365X02007951"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,5]]},"references-count":35,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2003,5]]}},"alternative-id":["S0012365X02007951"],"URL":"https:\/\/doi.org\/10.1016\/s0012-365x(02)00795-1","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[2003,5]]}}}