Abstract
Letn≧k≧t be positive integers, andX—a set ofn elements. LetC(n, k, t) be the smallest integerm such that there existm k-tuples ofX B1B2,...,Bm with the property that everyt-tuple ofX is contained in at least oneBi. It is shown that in many cases the standard lower bound forC(n, k, 2) can be improved (k sufficiently large,n/k being fixed). Some exact values ofC(n, k, 2) are also obtained.
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