Minimum embedding of STSs into (K3+e)-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 K3-design of order v can be embedded into a (K3+e)-design of order n.