Existence of resolvable group divisible designs with block size four I Original Research Article

It is proved in this paper that for m≢0,2,6,10 (mod 12) there exists a resolvable group divisible design of order v, block size 4 and group size m if and only v≡0 (mod 4), v≡0 (mod m), v−m≡0 (mod 3), except when (m,v)=(3,12) and except possibly when (3,264), (3,372), (8,80), (8,104), (9,396) (40,400) or (40,520).