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Designs, Codes and Cryptography

, Volume 10, Issue 3, pp 275–307 | Cite as

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

  • R. J. R. Abel
  • Charles J. Colbourn
  • Jianxing Yin
  • Hantao Zhang
Article

Abstract

The basic necessary condition for the existence of a TD(5, λ; v)-TD(5, λ; u), namely v ≥ 4u, is shown to be sufficient for any λ ≥ 1, except when (v, u) = (6, 1) and λ = 1, and possibly when (v, 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.

transversal design latin square group divisible design pairwise balanced design orthgonal array 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • R. J. R. Abel
    • 1
  • Charles J. Colbourn
    • 2
  • Jianxing Yin
    • 3
  • Hantao Zhang
    • 4
  1. 1.School of MathematicsUniversity of New South WalesKensingtonAustralia
  2. 2.Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  3. 3.Department of MathematicsSuzhou UniversitySuzhouPeople's Republic of China
  4. 4.Computer ScienceUniversity of IowaIowa CityU.S.A

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