{"title":"准对称（2）-（（28,12,11））设计与阶（5）的自动形态","authors":"Renata Vlahovic Kruc, Vedran Krčadinac","doi":"10.3336/gm.58.2.01","DOIUrl":null,"url":null,"abstract":"A design is called quasi-symmetric if it has only two block intersection numbers. Using a method based on orbit matrices, we classify quasi-symmetric \\(2\\)-\\((28,12,11)\\) designs with intersection numbers \\(4\\), \\(6\\), and an automorphism of order \\(5\\). There are exactly \\(31\\,696\\) such designs up to isomorphism.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-symmetric \\\\(2\\\\)-\\\\((28,12,11)\\\\) designs with an automorphism of order \\\\(5\\\\)\",\"authors\":\"Renata Vlahovic Kruc, Vedran Krčadinac\",\"doi\":\"10.3336/gm.58.2.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A design is called quasi-symmetric if it has only two block intersection numbers. Using a method based on orbit matrices, we classify quasi-symmetric \\\\(2\\\\)-\\\\((28,12,11)\\\\) designs with intersection numbers \\\\(4\\\\), \\\\(6\\\\), and an automorphism of order \\\\(5\\\\). There are exactly \\\\(31\\\\,696\\\\) such designs up to isomorphism.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3336/gm.58.2.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3336/gm.58.2.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quasi-symmetric \(2\)-\((28,12,11)\) designs with an automorphism of order \(5\)
A design is called quasi-symmetric if it has only two block intersection numbers. Using a method based on orbit matrices, we classify quasi-symmetric \(2\)-\((28,12,11)\) designs with intersection numbers \(4\), \(6\), and an automorphism of order \(5\). There are exactly \(31\,696\) such designs up to isomorphism.
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