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

In this paper, we continue the investigation for the existence of resolvable group divisible designs 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 depends mainly on the cases h=1, 2, 3, 6 and 12. Up to now, more than half of these cases have been solved or almost solved except for h=2 and 6. We shall show that the above necessary conditions are also sufficient for h=6 except n=4 and possibly excepting n∈{6,52,54,58,62,68,74,102,114,124}.