Resolvable Modified Group Divisible Designs with Block Size Three

Resolvable holey group divisible designs with block size three

Class-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs

We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master de...

Resolvable group divisible designs with block size 3

A group divisible design is resolvable if there exists a partition n = {P,, Pz, . .} of p such that each part Pi is itself a partition of X. In this paper we investigate the existence of resolvable group divisible designs with K = {3}, M a singleton set, and all A. The case where M = { 1) has been solved by Ray-Chaudhuri and Wilson for I = 1, and by Hanani for all h > 1. The case where M is a s...

Existence of resolvable group divisible designs with block size four I

It is proved in this paper that for m ≡ 0; 2; 6; 10 (mod 12) there exists a resolvable group divisible design of order v, block size 4 and group size m if and only v ≡ 0 (mod 4), v ≡ 0 (modm), v − m ≡ 0 (mod 3), except when (3; 12) and except possibly when (3; 264); (3; 372); (8; 80); (8; 104), (9; 396) (40; 400) or (40; 520). c © 2002 Elsevier Science B.V. All rights reserved.

Resolvable modified group divisible designs with higher index

A resolvable modified group divisible design (RMGD) is a modified group divisible design whose blocks can be partitioned into parallel classes. We show that the necessary conditions for the existence of a 3-RMGDDλ of type g, namely g ≥ 3, u ≥ 3, gu ≡ 0 mod 3 and λ(g−1)(u−1) ≡ 0 mod 2, are sufficient with the two exceptions of (g, u, λ) ∈ {(6, 3, 1), (3, 6, 1)}.