Asymptotically good coverings
Using a probability argument, the author gives an alternative proof to the result, known originally as the Erdős-Hanani conjecture, that, for fixed r, k, \(r<k\), and n large enough, there exists a covering of all r- sets of an n-set by a family of k-sets whose cardinality is asymptotically \(\left( \begin{matrix} n\\ r\end{matrix} \right)/\left( \begin{matrix} k\\ r\end{matrix} \right)\) with respect to n.
scientific article; zbMATH DE number 3924791