Existence of Incomplete Transversal Designs with BlockSize Five and Any Index λ

Authors:
R. J. R. Abel;Charles J. Colbourn;Jianxing Yin;Hantao Zhang
Affiliations:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia;Combinatoricsand Optimization, University of Waterloo, Waterloo, Ontario,Canada N2L 3G1;Department of Mathematics, Suzhou University, Suzhou 215006, People‘s Republic of China;Computer Science, University of Iowa, Iowa City, Iowa 52242, U.S.A.
Venue:
Designs, Codes and Cryptography
Year:
1997

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Abstract

The basic necessary condition forthe existence of a TD(5, λ; v)-TD(5, λ; u),namely v ≥ 4u, is shown to be sufficient forany 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, 86new incomplete transversal designs are constructed. Several constructiontechniques are developed, and some new incomplete TDs with blocksize six and seven are also presented.