Existence of resolvable group divisible designs with block size four I

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 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...

Resolvable Modified Group Divisible Designs with Block Size Three

A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. # 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007

Resolvable holey group divisible designs with block size three

Group divisible designs with block size four and two groups

We give some constructions of new infinite families of group divisible designs, GDD(n, 2, 4; 1, 2), including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for 3 n 8. For n= 10 there is one missing critical design. If 1> 2, then the necessary conditions are sufficient for n ≡ 4, 5, 8 (mod 12). For each of n=10, 15, 16, 17, 18, 19, and 20 we...