Group divisible covering designs with block size four

Hengjia Wei, Gennian Ge, Charles Colbourn

Research output: Contribution to journalArticle

Abstract

Group divisible covering designs (GDCDs) were introduced by Heinrich and Yin as a natural generalization of both covering designs and group divisible designs. They have applications in software testing and universal data compression. The minimum number of blocks in a k-GDCD of type gu is a covering number denoted by C(k, gu). When k = 3, the values of C(3, gu) have been determined completely for all possible pairs (g, u). When k = 4, Francetić et al. constructed many families of optimal GDCDs, but the determination remained far from complete. In this paper, two specific 4-IGDDs are constructed, thereby completing the existence problem for 4-IGDDs of type (g, h)u. Then, additional families of optimal 4-GDCDs are constructed. Consequently the cases for (g, u) whose status remains undetermined arise when g ≡ 11, 14, 17, 23 and 24, when u ≡ 5 and 6, and in several small families for which one of g and u is fixed.

Original languageEnglish (US)
Pages (from-to)101-118
Number of pages18
JournalJournal of Combinatorial Designs
Volume26
Issue number3
DOIs
StatePublished - Mar 2018

Keywords

  • covering numbers
  • group divisible covering designs
  • group divisible designs
  • incomplete group divisible designs
  • primary 05B05

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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