Minimum embedding of P3P3-designs into TS(v,λ)TS(v,λ)

A triple system of order v+wv+w and index λλembeds   a P3P3-design on vv points if there is a subset of vv points on which the K3K3-blocks induce the blocks of a P3P3-design. In this paper is settled the minimum embedding of a P3P3-design of order vv into a TS(v+w,λ)TS(v+w,λ).