The existence of uniform 5-GDDs

Jianxing Yin, Alan C.H. Ling, Charles J. Colbourn, R. J.R. Abel

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

In this article, we construct group divisible designs (GDDs) with block size five, group-type gu and index unity. The necessary condition for the existence of such a GDD is u > 5, (u - 1)g ≡ 0 (mod 4) and u(u - 1)g2 ≡ 0 (mod 20). It is shown that these necessary conditions are also sufficient, except possibly in a few cases. Additionally, a new construction to obtain GDDs using holey TDs is presented.

Original languageEnglish (US)
Pages (from-to)275-299
Number of pages25
JournalJournal of Combinatorial Designs
Volume5
Issue number4
DOIs
StatePublished - Jan 1 1997
Externally publishedYes

Keywords

  • Group divisible design
  • Pairwise balanced design

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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