On the difference between asymptotically good packings and coverings (Q1345524)

It is proved that asymptotically ``good'' coverings of \(l\)-subsets of an \(n\)-set by \(k\)-subsets \((l< k< n)\) exist for \(k= o(n)\) and slowly increasing \(l\). Moreover, if \(l= o(k)\) then asymptotically good packings do not exist if \(k> c\sqrt n\) for some constant \(c> 1\), and do exist if \(k< e\sqrt n\) for some \(c< 1\).