Design theory
Resolvable group divisible designs with block size 3
Discrete Mathematics - Combinatorial designs: a tribute to Haim Hanani
Resolvable group divisible designs with block size four
Discrete Mathematics
A systematic approach to some block design constructions
Journal of Combinatorial Theory Series A
Group divisible designs with block size four and group type gum1 with minimum m
Designs, Codes and Cryptography
Resolvable maximum packings with quadruples
Designs, Codes and Cryptography
Journal of Combinatorial Theory Series A
Embeddings of resolvable group divisible designs with block size 3
Designs, Codes and Cryptography
Kirkman frames having hole type hum1 for small h
Designs, Codes and Cryptography
On uniformly resolvable designs with block sizes 3 and 4
Designs, Codes and Cryptography
| Hi-index | 0.05 |
In this paper, we continue the investigation for the existence of resolvable group divisible designs with block size four, group-type hn and index unity. The necessary conditions for such a design are n ≥ 4, hn ≡ 0(mod 4) and h(n - 1) ≡ 0(mod 3). The existence of these designs depends mainly on the cases h = 1, 2, 3, 6 and 12. Up to now, more than half of these cases have been solved or almost solved except for h = 2 and 6. We shall show that the above necessary conditions are also sufficient for h = 6 except n = 4 and possibly excepting n ∈ {6, 52, 54, 58, 62, 68, 74, 102, 114, 124}.