Embeddings of maximum packings in triple systems

Abstract

Let MPT(v,lambda) denote a maximum packing of triples of order v with index lambda and TS(u, lambda) denote a triple system of order u with index lambda. For lambda > 1 and v greater than or equal to 6, it is proved in this paper that the necessary and sufficient conditions for the embedding of an MPT(v, lambda) in a TS(u, lambda) are lambda(u - 1) equivalent to 0 (mod 2), lambdau(u - 1) equivalent to 0 (mod 6) and u greater than or equal to 2v + 1. (C) 2003 Published by Elsevier B.V.