Existence of resolvable group divisible designs with block size four I

Abstract 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).