Minimum embedding of a KS(u,λ) into a KS(u+w,μ)

Let HH be a subgraph of a graph GG. An HH-design (U,C)(U,C) of order uu and index λλ is embedded into a GG-design (V,B)(V,B) of order vv and index μμ if λ≤μλ≤μ, U⊆VU⊆V and there is an injective mapping f:C→Bf:C→B such that BB is a subgraph of f(B)f(B) for every B∈CB∈C. The mapping ff is called the embedding of (U,C)(U,C) into (V,B)(V,B). In this paper, we study the minimum embedding of a kite system of order uu and index λλ (denoted by KS(u,λ)) into a kite system of order u+wu+w and index μμ.