An upper bound for the lengths of arcs in Steiner systems is given. A partial Steiner system PS t; k; v is a pair W; b where W is a set of v points and b a set of k-subsets (called blocks) of W such that any t-subset of W is contained in at most one block. A Steiner system S t; k; v is a partial Steiner system such that any t-subset is contained in… (More)