TY - JOUR
T1 - Existence of Incomplete Transversal Designs with Block Size Five and Any Index λ
AU - Abel, R. J.R.
AU - Colbourn, Charles J.
AU - Yin, Jianxing
AU - Zhang, Hantao
N1 - Funding Information:
This research is supported by the Natural Sciences and Engineering Research Council of Canada under Grant A0579 to the second author. This paper was written while the third author was visiting the Department of Combinatorics and Optimization, University of Waterloo. The hospitality of the Department is gratefully acknowledged. The fourth author is partially supported by the National Science Foundation under grants CCR-9202838 and CCR-9357851.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1997
Y1 - 1997
N2 - 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.
AB - 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.
KW - Group divisible design
KW - Latin square
KW - Orthgonal array
KW - Pairwise balanced design
KW - Transversal design
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U2 - 10.1023/A:1008232418845
DO - 10.1023/A:1008232418845
M3 - Article
AN - SCOPUS:0013524544
VL - 10
SP - 275
EP - 307
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
SN - 0925-1022
IS - 3
ER -