A survey on resolvable group divisible designs with block size four

In this paper, a survey for the existence of resolvable group divisible designs (RGDDs) with block size four, group-type h n and index unity is presented. It is proved that there exists a 4-RGDD of type h n if and only if n⩾4, hn≡0 ( mod 4) and h(n−1)≡0 ( mod 3) with a handful of possible exceptions...

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Bibliographic Details
Published in:Discrete mathematics 2004-03, Vol.279 (1), p.225-245
Main Authors: Ge, Gennian, Ling, Alan C.H
Format: Article
Language:English
Subjects:
4-frames
Algebra
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Group divisible designs
Incomplete resolvable group divisible designs
Mathematics
Resolvable group divisible designs
Sciences and techniques of general use
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Summary:In this paper, a survey for the existence of resolvable group divisible designs (RGDDs) with block size four, group-type h n and index unity is presented. It is proved that there exists a 4-RGDD of type h n if and only if n⩾4, hn≡0 ( mod 4) and h(n−1)≡0 ( mod 3) with a handful of possible exceptions.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(03)00274-7