Embeddings of maximum packings in triple systems Original Research Article

Let MPT(v,λ) denote a maximum packing of triples of order v with index λ and TS(u,λ) denote a triple system of order u with index λ. For λ>1 and v⩾6, it is proved in this paper that the necessary and sufficient conditions for the embedding of an MPT(v,λ) in a TS(u,λ) are λ(u−1)≡0 (mod 2), λu(u−1)≡0 (mod 6) and u⩾2v+1.