Improving the Existence Bounds for Grid-Block Difference Families
Improving the Existence Bounds for Grid-Block Difference Families
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DOI：
10.1007/s00373-017-1776-5
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发表时间：
2017-04
影响因子：
0.7
通讯作者：
Xiaonan Lu
中科院分区：
文献类型：
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作者：
Xiaonan Lu
本文利用乘性和的韦尔定理，提出了有限域中满足一定分圆条件的元素存在界的中间代数推论。在许多情况下，由于 Buratti 和 Pasotti (Finite Fields Appl 15(3), 332–344, 2009)，这种方法改进了界限，可广泛用于显示具有点正则自同构的组合设计的渐近存在性。此外，该方法还应用于改进网格块差异族的存在界，可以将其视为差异族的推广。
In this paper, by employing Weil’s Theorem on multiplicative character sums, an intermediate algebraic consequence on the existence bound of an element satisfying certain cyclotomic conditions in a finite field is proposed. In many cases, this approach improves the bound due to Buratti and Pasotti (Finite Fields Appl 15(3), 332–344, 2009), which can be widely used for showing the asymptotic existence of combinatorial designs with point-regular automorphisms. Moreover, this approach is applied to improving the existence bound for grid-block difference families, which can be regarded as generalizations of difference families.