Existence of Incomplete Transversal Designs with Block Size Five and Any Index λ

R. J.R. Abel, Charles J. Colbourn, Jianxing Yin, Hantao Zhang

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

The basic necessary condition for the existence of a T D (5, λ; υ) - T D (5, λ; u), namely υ ≥ 4u, is shown to be sufficient for any λ ≥ 1, except when (υ, u) = (6, 1) and λ = 1, and possibly when (υ, u) = (10, 1) or (52, 6) and λ = 1. For the case λ = 1, 86 new incomplete transversal designs are constructed. Several construction techniques are developed, and some new incomplete TDs with block size six and seven are also presented.

Original languageEnglish (US)
Pages (from-to)275-307
Number of pages33
JournalDesigns, Codes, and Cryptography
Volume10
Issue number3
DOIs
StatePublished - Jan 1 1997
Externally publishedYes

Keywords

  • Group divisible design
  • Latin square
  • Orthgonal array
  • Pairwise balanced design
  • Transversal design

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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