Given parameters n,k,p,t, and a base set X where |X|=n, an (n,k,p,t) Lotto design is a set of k-subsets of X (called blocks) such that every p-subset of X intersects at least one of the blocks in t or more elements. Let L(n,k,p,t) denote the smallest possible (in terms of number of blocks) (n,k,p,t) Lotto design.

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