{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T21:50:43Z","timestamp":1778795443397,"version":"3.51.4"},"reference-count":39,"publisher":"American Mathematical Society (AMS)","issue":"342","license":[{"start":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T00:00:00Z","timestamp":1709856000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["RG21\/20"],"award-info":[{"award-number":["RG21\/20"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["RG23\/20"],"award-info":[{"award-number":["RG23\/20"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["336005"],"award-info":[{"award-number":["336005"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["351271"],"award-info":[{"award-number":["351271"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001459","name":"Ministry of Education - Singapore","doi-asserted-by":"publisher","award":["PRIMUS\/20\/SCI\/002"],"award-info":[{"award-number":["PRIMUS\/20\/SCI\/002"]}],"id":[{"id":"10.13039\/501100001459","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["RG21\/20"],"award-info":[{"award-number":["RG21\/20"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["RG23\/20"],"award-info":[{"award-number":["RG23\/20"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["336005"],"award-info":[{"award-number":["336005"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["351271"],"award-info":[{"award-number":["351271"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["PRIMUS\/20\/SCI\/002"],"award-info":[{"award-number":["PRIMUS\/20\/SCI\/002"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007397","name":"Univerzita Karlova v Praze","doi-asserted-by":"publisher","award":["RG21\/20"],"award-info":[{"award-number":["RG21\/20"]}],"id":[{"id":"10.13039\/100007397","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007397","name":"Univerzita Karlova v Praze","doi-asserted-by":"publisher","award":["RG23\/20"],"award-info":[{"award-number":["RG23\/20"]}],"id":[{"id":"10.13039\/100007397","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007397","name":"Univerzita Karlova v Praze","doi-asserted-by":"publisher","award":["336005"],"award-info":[{"award-number":["336005"]}],"id":[{"id":"10.13039\/100007397","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007397","name":"Univerzita Karlova v Praze","doi-asserted-by":"publisher","award":["351271"],"award-info":[{"award-number":["351271"]}],"id":[{"id":"10.13039\/100007397","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007397","name":"Univerzita Karlova v Praze","doi-asserted-by":"publisher","award":["PRIMUS\/20\/SCI\/002"],"award-info":[{"award-number":["PRIMUS\/20\/SCI\/002"]}],"id":[{"id":"10.13039\/100007397","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construction, we improve the lower bound on the maximum cardinality of an equiangular line system in 18 dimensions to 57.<\/p>","DOI":"10.1090\/mcom\/3832","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T08:16:22Z","timestamp":1675930582000},"page":"1867-1903","source":"Crossref","is-referenced-by-count":6,"title":["Equiangular lines in Euclidean spaces: Dimensions 17 and 18"],"prefix":"10.1090","volume":"92","author":[{"given":"Gary","family":"Greaves","sequence":"first","affiliation":[]},{"given":"Jeven","family":"Syatriadi","sequence":"additional","affiliation":[]},{"given":"Pavlo","family":"Yatsyna","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,3,8]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1016\/j.laa.2018.07.019","article-title":"There is no (75,32,10,16) strongly regular graph","volume":"557","author":"Azarija, Jernej","year":"2018","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"issue":"4","key":"2","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1002\/jcd.21696","article-title":"There is no (95,40,12,20) strongly regular graph","volume":"28","author":"Azarija, Jernej","year":"2020","journal-title":"J. Combin. Des.","ISSN":"https:\/\/id.crossref.org\/issn\/1063-8539","issn-type":"print"},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s00222-017-0746-0","article-title":"Equiangular lines and spherical codes in Euclidean space","volume":"211","author":"Balla, Igor","year":"2018","journal-title":"Invent. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0020-9910","issn-type":"print"},{"issue":"1","key":"4","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1137\/15M1036920","article-title":"Bounds on equiangular lines and on related spherical codes","volume":"30","author":"Bukh, Boris","year":"2016","journal-title":"SIAM J. Discrete Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4801","issn-type":"print"},{"issue":"3-4","key":"5","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","article-title":"The Magma algebra system. I. The user language","volume":"24","author":"Bosma, Wieb","year":"1997","journal-title":"J. Symbolic Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0747-7171","issn-type":"print"},{"issue":"5","key":"6","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/S0195-6698(89)80014-9","article-title":"A (49,16,3,6) strongly regular graph does not exist","volume":"10","author":"Bussemaker, F. C.","year":"1989","journal-title":"European J. Combin.","ISSN":"https:\/\/id.crossref.org\/issn\/0195-6698","issn-type":"print"},{"key":"7","unstructured":"A.-L. Cauchy, Sur l\u2019\u00e9quation \u00e0 l\u2019aide de laquelle on d\u00e9termine les in\u00e9galit\u00e9s s\u00e9culaires des mouvements des plan\u00e8tes, In \u0152uvres compl\u00e8tes, IIi\u00e8me S\u00e9rie, Gauthier-Villars, Paris, 1829."},{"key":"8","series-title":"Encyclopedia of Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139086547","volume-title":"Eigenspaces of graphs","volume":"66","author":"Cvetkovi\u0107, D.","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/0521573521"},{"issue":"1","key":"9","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1090\/bull\/1722","article-title":"Eigenvectors from eigenvalues: a survey of a basic identity in linear algebra","volume":"59","author":"Denton, Peter B.","year":"2022","journal-title":"Bull. Amer. Math. Soc. (N.S.)","ISSN":"https:\/\/id.crossref.org\/issn\/0273-0979","issn-type":"print"},{"key":"10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1515\/crll.1902.124.1","article-title":"Theorie der einfachen Ungleichungen","volume":"124","author":"Farkas, Julius","year":"1902","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"11","unstructured":"S. Fisk, A very short proof of Cauchy\u2019s interlace theorem for eigenvalues of Hermitian matrices, Amer. Math. Monthly 112 (2005), no. 2, 118\u2013118."},{"issue":"3","key":"12","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0095-8956(81)90046-0","article-title":"Spectral conditions for the reconstructibility of a graph","volume":"30","author":"Godsil, C. D.","year":"1981","journal-title":"J. Combin. Theory Ser. B","ISSN":"https:\/\/id.crossref.org\/issn\/0095-8956","issn-type":"print"},{"key":"13","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic graph theory","volume":"207","author":"Godsil, Chris","year":"2001","ISBN":"https:\/\/id.crossref.org\/isbn\/0387952411"},{"key":"14","doi-asserted-by":"publisher","first-page":"810","DOI":"10.1016\/j.aim.2018.03.024","article-title":"Upper bounds for \ud835\udc60-distance sets and equiangular lines","volume":"330","author":"Glazyrin, Alexey","year":"2018","journal-title":"Adv. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-8708","issn-type":"print"},{"key":"15","doi-asserted-by":"crossref","unstructured":"G. R. W. Greaves, Magma companion code and computations from the paper \u201cEquiangular lines in Euclidean spaces: dimensions 17 and 18\u201d, \\url{https:\/\/github.com\/grwgrvs\/equiangular17\/}, (2023).","DOI":"10.1090\/mcom\/3832"},{"key":"16","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.laa.2017.09.008","article-title":"Equiangular line systems and switching classes containing regular graphs","volume":"536","author":"Greaves, Gary R. W.","year":"2018","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"key":"17","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jcta.2015.09.008","article-title":"Equiangular lines in Euclidean spaces","volume":"138","author":"Greaves, Gary","year":"2016","journal-title":"J. Combin. Theory Ser. A","ISSN":"https:\/\/id.crossref.org\/issn\/0097-3165","issn-type":"print"},{"issue":"6","key":"18","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1007\/s00493-020-4523-0","article-title":"Equiangular lines in low dimensional Euclidean spaces","volume":"41","author":"Greaves, Gary R. W.","year":"2021","journal-title":"Combinatorica","ISSN":"https:\/\/id.crossref.org\/issn\/0209-9683","issn-type":"print"},{"key":"19","doi-asserted-by":"crossref","unstructured":"G. R. W. Greaves, J. Syatriadi, and P. Yatsyna, Equiangular lines in Euclidean spaces: dimensions 17 and 18,  arXiv:2104.04330, (2023).","DOI":"10.1090\/mcom\/3832"},{"issue":"320","key":"20","doi-asserted-by":"publisher","first-page":"3041","DOI":"10.1090\/mcom\/3433","article-title":"On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix","volume":"88","author":"Greaves, Gary R. W.","year":"2019","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"21","first-page":"355","article-title":"Equilateral point-sets in elliptic two- and three-dimensional spaces","volume":"22","author":"Haantjes, J.","year":"1948","journal-title":"Nieuw Arch. Wiskunde (2)"},{"issue":"2","key":"22","doi-asserted-by":"publisher","first-page":"157","DOI":"10.2307\/4145217","article-title":"Cauchy\u2019s interlace theorem for eigenvalues of Hermitian matrices","volume":"111","author":"Hwang, Suk-Geun","year":"2004","journal-title":"Amer. Math. Monthly","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9890","issn-type":"print"},{"issue":"1","key":"23","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/s11856-020-1983-2","article-title":"Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines","volume":"236","author":"Jiang, Zilin","year":"2020","journal-title":"Israel J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-2172","issn-type":"print"},{"issue":"3","key":"24","doi-asserted-by":"publisher","first-page":"729","DOI":"10.4007\/annals.2021.194.3.3","article-title":"Equiangular lines with a fixed angle","volume":"194","author":"Jiang, Zilin","year":"2021","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"issue":"4","key":"25","doi-asserted-by":"publisher","first-page":"2479","DOI":"10.1137\/19M1248881","article-title":"New upper bounds for equiangular lines by pillar decomposition","volume":"33","author":"King, Emily J.","year":"2019","journal-title":"SIAM J. Discrete Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4801","issn-type":"print"},{"issue":"1-2","key":"26","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s10107-021-01638-x","article-title":"\ud835\udc58-point semidefinite programming bounds for equiangular lines","volume":"194","author":"de Laat, David","year":"2022","journal-title":"Math. Program.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5610","issn-type":"print"},{"key":"27","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1016\/0021-8693(73)90123-3","article-title":"Equiangular lines","volume":"24","author":"Lemmens, P. W. H.","year":"1973","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"28","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1016\/j.laa.2019.12.002","article-title":"Saturated configuration and new large construction of equiangular lines","volume":"588","author":"Lin, Yen-chi Roger","year":"2020","journal-title":"Linear Algebra Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0024-3795","issn-type":"print"},{"key":"29","first-page":"335","article-title":"Equilateral point sets in elliptic geometry","volume":"28","author":"van Lint, J. H.","year":"1966","journal-title":"Indag. Math."},{"key":"30","unstructured":"Wolfram Research, Inc., Mathematica, Version Number 10.0, Champaign, IL, 2014."},{"key":"31","isbn-type":"print","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/978-3-540-24847-7_25","article-title":"Salem numbers of trace -2 and traces of totally positive algebraic integers","author":"McKee, James","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/3540221565"},{"key":"32","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1016\/j.ejc.2015.11.003","article-title":"A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4","volume":"53","author":"Okuda, Takayuki","year":"2016","journal-title":"European J. Combin.","ISSN":"https:\/\/id.crossref.org\/issn\/0195-6698","issn-type":"print"},{"key":"33","first-page":"125","article-title":"Graphs and two-graphs","author":"Seidel, J. J.","year":"1974"},{"key":"34","unstructured":"N. J. A. Sloane (editor), The On-Line Encyclopedia of Integer Sequences. Published electronically at \\url{https:\/\/oeis.org\/}, (2023)."},{"issue":"1","key":"35","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1007\/s00454-017-9933-4","article-title":"A remark on a construction of D. S. Asche","volume":"61","author":"Sz\u00f6ll\u0151si, Ferenc","year":"2019","journal-title":"Discrete Comput. Geom.","ISSN":"https:\/\/id.crossref.org\/issn\/0179-5376","issn-type":"print"},{"issue":"2","key":"36","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1112\/plms\/s3-35.2.257","article-title":"Regular 2-graphs","volume":"35","author":"Taylor, D. E.","year":"1977","journal-title":"Proc. London Math. Soc. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0024-6115","issn-type":"print"},{"key":"37","doi-asserted-by":"crossref","first-page":"115","DOI":"10.6028\/jres.072B.015","article-title":"Principal submatrices. V. Some results concerning principal submatrices of arbitrary matrices","volume":"72B","author":"Thompson, R. C.","year":"1968","journal-title":"J. Res. Nat. Bur. Standards Sect. B","ISSN":"https:\/\/id.crossref.org\/issn\/0022-4340","issn-type":"print"},{"issue":"1","key":"38","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/BF02948947","article-title":"Die 5-fach transitiven gruppen von mathieu","volume":"12","author":"Witt, Ernst","year":"1937","journal-title":"Abh. Math. Sem. Univ. Hamburg","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5858","issn-type":"print"},{"issue":"2","key":"39","doi-asserted-by":"publisher","first-page":"908","DOI":"10.1137\/16M109377X","article-title":"New bounds for equiangular lines and spherical two-distance sets","volume":"31","author":"Yu, Wei-Hsuan","year":"2017","journal-title":"SIAM J. Discrete Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0895-4801","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03832-7\/mcom3832_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03832-7\/S0025-5718-2023-03832-7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:58:58Z","timestamp":1776833938000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-342\/S0025-5718-2023-03832-7\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,8]]},"references-count":39,"journal-issue":{"issue":"342","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["S0025-5718-2023-03832-7"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3832","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2023,3,8]]}}}