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≡7mod12 and u≡3mod6, when g≡11,14,17,23mod24 and u≡5mod6, and in several small families for which one of g and u is fixed.

Original languageEnglish (US)
JournalJournal of Combinatorial Designs
DOIs
StateAccepted/In press - Jan 1 2017

Fingerprint

Divisible
Covering
Group Divisible Design
Covering number
Software Testing
K-group
Data Compression
Design
Family

Keywords

  • Covering numbers
  • Group divisible covering designs
  • Group divisible designs
  • Incomplete group divisible designs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Group divisible covering designs with block size four. / Wei, Hengjia; Ge, Gennian; Colbourn, Charles.

In: Journal of Combinatorial Designs, 01.01.2017.

Research output: Contribution to journalArticle

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