Group divisible designs with block size four and group type g um1 for g ≡ 0 mod 6

Hengjia Wei, Gennian Ge

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Nonuniform group divisible designs (GDDs) have been studied by numerous researchers for the past two decades due to their essential role in the constructions for other types of designs. In this paper, we investigate the existence problem of {4}-GDDs of type gum1 for g≡0mod6. First, we determine completely the spectrum of {4}-GDDs of types 18um1 and 36um1. Furthermore, for general cases, we show that for each g≡0mod6 and g≥12, a {4}-GDD of type gum1 exists if and only if u≥4, m≡0mod3 and 0≤m≤g(u-1)/2, except possibly for g≡6,42,66,78,102,114,138, 174mod180, g≥42 and (u,m){(7,3g-3),(11,5g-9),(11,5g-6),(11,5g-3),(13,6g-9), (13,6g-3)}.

Original languageEnglish
Pages (from-to)26-52
Number of pages27
JournalJournal of Combinatorial Designs
Volume22
Issue number1
DOIs
StatePublished - 1 Jan 2014
Externally publishedYes

Keywords

  • double group divisible designs
  • group divisible designs
  • incomplete group divisible designs

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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