Resolvable group divisible designs with block size four and index three Original Research Article

In this paper, we investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type hnhn and index three. The necessary conditions for the existence of such a design are n⩾4n⩾4 and hn≡0hn≡0View the MathML source(mod4). These necessary conditions are shown to be sufficient except for (h,n)∈{(2,4),(2,6)}(h,n)∈{(2,4),(2,6)} and possibly excepting (h,n)=(2,54)(h,n)=(2,54).