Minimum embedding of STSs into -systems

A G -design ( V , B ) is called embedded into a H -design ( V ∪ W , D ) if G is a subgraph of H and there is an injective mapping f : B → D such that B is a subgraph of f ( B ) for every B ∈ B . The purpose of this note is to determine, for each admissible v , the minimum integer n such that any K 3 -design of order v can be embedded into a ( K 3 + e ) -design of order n .