α-resolvable group divisible designs with block size four and groups size six and nine

Abstract

A group divisible design GD(k, γ, t; tn) is α-resolvable if its blocks can be partitioned into classes such that each point of the design occurs in precisely α blocks in each class. The necessary conditions for the existence of such a design are n ≥ k, γt(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 = 6 and 9, except for some possible exceptions.