{"title":"关于正交拉丁方的个数","authors":"Haim Hanani","doi":"10.1016/S0021-9800(70)80079-5","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>N(n)</em> be the maximal number of mutually orthogonal Latin squares of order <em>n</em> and let <em>n<sub>r</sub></em> be the smallest integer such that <em>N(n)≥r</em> for every <em>n>n<sub>r</sub></em>. It is known that <em>N(n)</em>→∞ as <em>n</em>→∞ and that <em>n</em><sub>2</sub>=6. A proof is given for <em>n</em><sub>3</sub>≤51, <em>n</em><sub>5</sub>≤62 and <em>n</em><sub>29</sub>≤34, 115, 553.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 3","pages":"Pages 247-271"},"PeriodicalIF":0.0000,"publicationDate":"1970-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80079-5","citationCount":"23","resultStr":"{\"title\":\"On the number of orthogonal latin squares\",\"authors\":\"Haim Hanani\",\"doi\":\"10.1016/S0021-9800(70)80079-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <em>N(n)</em> be the maximal number of mutually orthogonal Latin squares of order <em>n</em> and let <em>n<sub>r</sub></em> be the smallest integer such that <em>N(n)≥r</em> for every <em>n>n<sub>r</sub></em>. It is known that <em>N(n)</em>→∞ as <em>n</em>→∞ and that <em>n</em><sub>2</sub>=6. A proof is given for <em>n</em><sub>3</sub>≤51, <em>n</em><sub>5</sub>≤62 and <em>n</em><sub>29</sub>≤34, 115, 553.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"8 3\",\"pages\":\"Pages 247-271\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80079-5\",\"citationCount\":\"23\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800795\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021980070800795","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let N(n) be the maximal number of mutually orthogonal Latin squares of order n and let nr be the smallest integer such that N(n)≥r for every n>nr. It is known that N(n)→∞ as n→∞ and that n2=6. A proof is given for n3≤51, n5≤62 and n29≤34, 115, 553.
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