The existence of uniform 5-GDDs

Jianxing Yin; Alan C.H. Ling; Charles J. Colbourn; R. J.R. Abel

doi:10.1002/(SICI)1520-6610(1997)5:4<275::AID-JCD4>3.0.CO;2-C

The existence of uniform 5-GDDs

Jianxing Yin, Alan C.H. Ling, Charles J. Colbourn, R. J.R. Abel

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

In this article, we construct group divisible designs (GDDs) with block size five, group-type g^u and index unity. The necessary condition for the existence of such a GDD is u > 5, (u - 1)g ≡ 0 (mod 4) and u(u - 1)g² ≡ 0 (mod 20). It is shown that these necessary conditions are also sufficient, except possibly in a few cases. Additionally, a new construction to obtain GDDs using holey TDs is presented.

Original language	English (US)
Pages (from-to)	275-299
Number of pages	25
Journal	Journal of Combinatorial Designs
Volume	5
Issue number	4
DOIs	https://doi.org/10.1002/(SICI)1520-6610(1997)5:4<275::AID-JCD4>3.0.CO;2-C
State	Published - Jan 1 1997
Externally published	Yes

Keywords

Group divisible design
Pairwise balanced design

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1002/(SICI)1520-6610(1997)5:4<275::AID-JCD4>3.0.CO;2-C

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AU - Yin, Jianxing

AU - Ling, Alan C.H.

AU - Colbourn, Charles J.

AU - Abel, R. J.R.

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Y1 - 1997/1/1

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AB - In this article, we construct group divisible designs (GDDs) with block size five, group-type gu and index unity. The necessary condition for the existence of such a GDD is u > 5, (u - 1)g ≡ 0 (mod 4) and u(u - 1)g2 ≡ 0 (mod 20). It is shown that these necessary conditions are also sufficient, except possibly in a few cases. Additionally, a new construction to obtain GDDs using holey TDs is presented.

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KW - Pairwise balanced design

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The existence of uniform 5-GDDs

Abstract

Keywords

ASJC Scopus subject areas

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