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

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

doi:10.1023/A:1008232418845

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 journal › Article › peer-review

25 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 language	English (US)
Pages (from-to)	275-307
Number of pages	33
Journal	Designs, Codes, and Cryptography
Volume	10
Issue number	3
DOIs	https://doi.org/10.1023/A:1008232418845
State	Published - 1997
Externally published	Yes

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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10.1023/A:1008232418845

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title = "Existence of Incomplete Transversal Designs with Block Size Five and Any Index λ",

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.",

keywords = "Group divisible design, Latin square, Orthgonal array, Pairwise balanced design, Transversal design",

author = "Abel, {R. J.R.} and Colbourn, {Charles J.} and Jianxing Yin and Hantao Zhang",

note = "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.",

year = "1997",

doi = "10.1023/A:1008232418845",

language = "English (US)",

volume = "10",

pages = "275--307",

journal = "Designs, Codes, and Cryptography",

issn = "0925-1022",

publisher = "Springer Netherlands",

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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.

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

Abstract

Keywords

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