A \(t\)-(n, k, \(\lambda\)) covering design consists of a collection of \(k\)-element subsets (blocks) of an \(n\)-element set \(\chi\) such that each \(t\)-element subset of \(\chi\) occurs in at least \(\lambda\) blocks. We use probabilistic techniques to obtain a general upper bound for the minimum size of such designs, extending a result of Erdős and Spencer [4].
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