On resolvable designs \(S_ 3(3;4,v)\) (Q1104925)

We study a method of Lonz and Vanstone which constructs an \(S_ 3(3,4,2n)\) from any given 1-factorization of \(K_{2n}\). We show that the resulting designs admit at least 3 mutually orthogonal resolutions whenever \(n\geq 4\) is even. In particular, the necessary conditions for the existence of a resolvable \(S_ 3(3,4,v)\) are also sufficient. Examples without repeated blocks are shown to exist provided that \(n\not\equiv 2\) mod 3.