On the difference between asymptotically good packings and coverings

It is proved that asymptotically good coverings of l-tuples of an n-element set by k-tuples exist for k = o(n) and slowly increasing l. On the other hand, it is noted that for l = o(k) asymptotically good packings do not exist if k > c√n for some constant c > 1 and exist for slowly increasing l if k < c√n for some constant c < 1.