Nonexistence results for tight block designs
Nonexistence results for tight block designs
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DOI：
10.1007/s10801-012-0395-8
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发表时间：
2011-10
影响因子：
0.8
通讯作者：
P. Dukes;Jesse Short-Gershman
中科院分区：
文献类型：
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作者：
P. Dukes;Jesse Short-Gershman
Recall that combinatorial 2s-designs admit a classical lower boundon their number of blocks, and that a design meeting this bound is called tight. A long-standing result of Bannai is that there exist only finitely many nontrivial tight 2s-designs for each fixeds≥5, although no concrete understanding of ‘finitely many’ is given. Here, we use the Smith Bound on approximate polynomial zeros to quantify this asymptotic nonexistence. Then, we outline and employ a computer search over the remaining parameter sets to establish (as expected) that there are in fact no such designs for 5≤s≤9, although the same analysis could in principle be extended to largers. Additionally, we obtain strong necessary conditions for existence in the difficult cases=4.
