On the Number of Sets in a Null t-Design

Let X be an nelement set, and let k, t, A be positive integers, n ~ k ~ t. A system Y of k-element subsets of X is called an SA (n, k, t) Steiner-system if every t-element subset of X is contained in exactly A members of Y. (Notice that two members of Yare not necessarily distinct.) We denote by hy the characteristic function of Y i.e. hy is defined on all subsets of X, and for any B ~X, h(B) is the number of occurences of Bin Y. Further, let V(X) denote the vector space of all real valued functions I: 2x ~ R. (Obviously, dim V(X) = 2".)