α-Resolvable Group DivisibleDesigns with Block Size Fourand Groups Size Six and Nine

摘要

A group divisible design GD(k, λ, t; tn) is a-resolvable if its blockscan be partitioned into classes such that each point of the designoccurs in precisely a blocks in each class. The necessary conditionsfor 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 conditionsare also sufficient when k = 4 and t = 6 and 9, except for somepossible exceptions.