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

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
State	Published - 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

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title = "The existence of uniform 5-GDDs",

abstract = "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.",

keywords = "Group divisible design, Pairwise balanced design",

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year = "1997",

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T1 - The existence of uniform 5-GDDs

AU - Yin, Jianxing

AU - Ling, Alan C.H.

AU - Colbourn, Charles J.

AU - Abel, R. J.R.

PY - 1997

Y1 - 1997

N2 - 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.

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.

KW - Group divisible design

KW - Pairwise balanced design

UR - https://www.scopus.com/pages/publications/0007128730

UR - https://www.scopus.com/pages/publications/0007128730#tab=citedBy

U2 - 10.1002/(SICI)1520-6610(1997)5:4

DO - 10.1002/(SICI)1520-6610(1997)5:4

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SP - 275

EP - 299

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 4

ER -

The existence of uniform 5-GDDs

Abstract

Keywords

ASJC Scopus subject areas

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