α-resolvable group divisible designs with block size four and group size three

Abstract

A group divisible design GD(k, λ, t; tn) is α-resolvable if its blocks can be partitioned into classes such that each point of the design occurs in precisely a blocks in each class. The necessary conditions for the existence of such a design are n ≥ k, λt(n - 1) = r(k- 1), bk = rtn, k\αtn and α\r. It is shown in this paper that these conditions are also sufficient when k = 4 and t = 3, except for n = 4 and α = λ = 1.