Large sets of subspace designs

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• 作者：Michael Braun^a ; ^{michael.braun@h-da.de} ; Michael Kiermaier^b ; ^{michael.kiermaier@uni-bayreuth.de} ; Axel Kohnert ; Reinhard Laue^c ; ^{laue@uni-bayreuth.de}
• 关键词：q-analog ; Combinatorial design ; Subspace design ; Large set ; Halving
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：147
• 期：Complete
• 页码：155-185
• 全文大小：609 K
• 卷排序：147

文摘

In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Graßmannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to subspace designs.We construct a 2-(6,3,78)5(6,3,78)5 design by computer, which corresponds to a halving LS5[2](2,3,6)LS5[2](2,3,6). The application of the new recursion method to this halving and an already known LS3[2](2,3,6)LS3[2](2,3,6) yields two infinite two-parameter series of halvings LS3[2](2,k,v)LS3[2](2,k,v) and LS5[2](2,k,v)LS5[2](2,k,v) with integers v≥6v≥6, v≡2(mod4) and 3≤k≤v−33≤k≤v−3, k≡3(mod4).Thus in particular, two new infinite series of nontrivial subspace designs with t=2t=2 are constructed. Furthermore as a corollary, we get the existence of infinitely many nontrivial large sets of subspace designs with t=2t=2.