Minimum embedding of a KS(u, lambda) into a KS(u+w, mu)

Let H be a subgraph of a graph G. An H-design (U, C) of order u and index lambda is embedded into a G-design (V, B) of order v and index mu if lambda <= mu, U subset of V and there is an injective mapping f : C -> B such that B is a subgraph of f (B) for every B is an element of C. The mapping f is called the embedding of (U, C) into (V. 2). In this paper, we study the minimum embedding of a kite system of order u and index lambda (denoted by KS(u, lambda)) into a kite system of order u + w and index mu.