Super-simple resolvable group divisible designs with block size 4 and index 2

Super-Simple Resolvable Balanced Incomplete Block Designs with Block Size 4 and Index 4

The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and v ≡ 4 (mod 12). These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007

Super-simple group divisible designs with block size 4 and index 5

In this paper, we investigate the existence of a super-simple (4, 5)-GDD of type gu and show that such a design exists if and only if u ≥ 4, g(u − 2) ≥ 10, g(u − 1) ≡ 0 (mod 3) and u(u− 1)g2 ≡ 0 (mod 12). © 2009 Elsevier 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