{"title":"关于不相交息差周期性产生的说明","authors":"N. Hamada, Teijiro Fukuda","doi":"10.32917/HMJ/1206138970","DOIUrl":null,"url":null,"abstract":"1. It is unknown whether the BIB design PG(ί = 2ra —1, 2): 1 obtained by choosing the points in PG (ί, 2) as treatments and all lines as blocks is resolvable or not for *;>5. C. R. Rao [1], [2] showed that the BIB design PG(ί = 3, 2): 1 with parameters t; = 15, ό = 35, k = 3, r=7, λ = l was resolvable by decomposing all lines in PG(3, 2) into 7 disjoint 1-fold spreads So, Su , S6. The procedure of constructing these spreads is as follows: (1) A set So consisting of 5 lines cyclically generated from the initial line L(x°, x, x) of the minimum cycle 0=5 is chosen as the initial 1-fold spread. (2) Generate Sj+X cyclically by a transformation (T(Sf)= Sj+ι (/=0, 1, ..., 5) where ΰ is a nonsingular linear transformation in PG(3, 2) such that","PeriodicalId":17080,"journal":{"name":"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry","volume":"77 1","pages":"191-194"},"PeriodicalIF":0.0000,"publicationDate":"1967-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on the cyclical generation of disjoint spreads\",\"authors\":\"N. Hamada, Teijiro Fukuda\",\"doi\":\"10.32917/HMJ/1206138970\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"1. It is unknown whether the BIB design PG(ί = 2ra —1, 2): 1 obtained by choosing the points in PG (ί, 2) as treatments and all lines as blocks is resolvable or not for *;>5. C. R. Rao [1], [2] showed that the BIB design PG(ί = 3, 2): 1 with parameters t; = 15, ό = 35, k = 3, r=7, λ = l was resolvable by decomposing all lines in PG(3, 2) into 7 disjoint 1-fold spreads So, Su , S6. The procedure of constructing these spreads is as follows: (1) A set So consisting of 5 lines cyclically generated from the initial line L(x°, x, x) of the minimum cycle 0=5 is chosen as the initial 1-fold spread. (2) Generate Sj+X cyclically by a transformation (T(Sf)= Sj+ι (/=0, 1, ..., 5) where ΰ is a nonsingular linear transformation in PG(3, 2) such that\",\"PeriodicalId\":17080,\"journal\":{\"name\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"volume\":\"77 1\",\"pages\":\"191-194\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1967-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of science of the Hiroshima University Ser. A Mathematics, physics, chemistry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32917/HMJ/1206138970\",\"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 science of the Hiroshima University Ser. A Mathematics, physics, chemistry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32917/HMJ/1206138970","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A note on the cyclical generation of disjoint spreads
1. It is unknown whether the BIB design PG(ί = 2ra —1, 2): 1 obtained by choosing the points in PG (ί, 2) as treatments and all lines as blocks is resolvable or not for *;>5. C. R. Rao [1], [2] showed that the BIB design PG(ί = 3, 2): 1 with parameters t; = 15, ό = 35, k = 3, r=7, λ = l was resolvable by decomposing all lines in PG(3, 2) into 7 disjoint 1-fold spreads So, Su , S6. The procedure of constructing these spreads is as follows: (1) A set So consisting of 5 lines cyclically generated from the initial line L(x°, x, x) of the minimum cycle 0=5 is chosen as the initial 1-fold spread. (2) Generate Sj+X cyclically by a transformation (T(Sf)= Sj+ι (/=0, 1, ..., 5) where ΰ is a nonsingular linear transformation in PG(3, 2) such that
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