Group divisible designs with block size four and group type gu m1

Hengjia Wei, Gennian Ge

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Non-uniform group divisible designs have been studied by numerous researchers in the past two decades due to their vital applications in the constructions for other types of designs. Much progress has been made for the existence of {4}-GDDs of type gu m1, especially when gu is even. The corresponding problem for block size three had been solved by Colbourn et al. (J Comb Theory Ser A 59:73–89, 1992). In this paper, we consider the entire existence problem for such {4}-GDDs. We show that, for each given g, up to a small number of undetermined cases of u, the necessary conditions on (u,m) for the existence of a {4}-GDD of type gu m1 are also sufficient.

Original languageEnglish
Pages (from-to)243-282
Number of pages40
JournalDesigns, Codes, and Cryptography
Issue number1
StatePublished - 1 Jan 2015
Externally publishedYes


  • Double group divisible designs
  • Group divisible designs
  • Incomplete group divisible designs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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