Improving the Existence Bounds for Grid-Block Difference Families

Xiao Nan Lu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)549-559
Number of pages11
JournalGraphs and Combinatorics
Volume33
Issue number3
DOIs
Publication statusPublished - 1 May 2017

Keywords

  • Difference family
  • Grid-block design
  • Weil’s Theorem on multiplicative character sums

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