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Group divisible designs with block size four and group type for more small.
- Source :
-
Discrete Mathematics . Oct2013, Vol. 313 Issue 20, p2065-2083. 19p. - Publication Year :
- 2013
-
Abstract
- Abstract: Non-uniform group divisible designs are instrumental in the constructions for other types of designs. Most of the progress for the existence of -GDDs of type is on the case when is even, where the existence for small has played a key role. In order to determine the spectrum for -GDDs of type with being odd, we continue to investigate the small cases with in this paper. We show that, for each , the necessary conditions for the existence of a -GDD of type are also sufficient. As the applications of these GDDs, we obtain a few pairwise balanced designs with minimum block size 4. Meanwhile, we also improve the existence result for frame self-orthogonal Mendelsohn triple systems of type by reducing an infinite class of possible exceptions, namely and , to eight undetermined cases. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 313
- Issue :
- 20
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 89607180
- Full Text :
- https://doi.org/10.1016/j.disc.2013.04.018