Resolvable group divisible designs with block size four Original Research Article

In this paper, we shall investigate the existence of resolvable group divisible designs (RGDDs) with block size four, group-type hn and index unity. The necessary conditions for such a design are n⩾4, hn≡0 (mod 4) and h(n−1)≡0 (mod 3). The existence of these designs mainly depends on the cases h=1,2,3,6 and 12. We shall improve the known results for the case h=3 and show that the above necessary conditions are also sufficient for h=3 except n=4 and possibly excepting n=88,124. We further show that these necessary conditions are also sufficient for h=12 except possibly n=17,18,23,27.