On resolvable designs S3(3; 4, v)

Abstract We study a method of Lonz and Vanstone which constructs an S 3 (3, 4, 2n) from any given 1-factorization of K 2 n . We show that the resulting designs admit at least 3 mutually orthogonal resolutions whenever n ⩾ 4 is even. In particular, the necessary conditions for the existence of a resolvable S 3 (3, 4, ν ) are also sufficient. Examples without repeated blocks are shown to exist provided that n ≢ 2 mod 3.