I'm working on an application for which I want to take the set $C$ of all the possible $k$-combinations of elements in $M$ (with $||M|| = m$), and cover $C$ with the sets of $k$-combinations of subsets $N_i$ of $M$, with $||N_i|| = n < m$ $\forall$ $N_i$

So there are $m \choose k$ combinations to cover, and each set $Q_i$ of $n$ elements will contain $n \choose k$ combinations.

What I'd like is an algorithm that constructs the sets $Q_i$ such that $q$ is minimized (i.e., as close to $m \choose k$ $/$ $n \choose k$ as possible)

So, for example, if $m = 100$, $k = 3$, and $n = 10$, I would want the smallest set of sets of $10$ elements such that their respective sets of $3$-combinations covered the set of $100 \choose 3$ $3$-combinations of M.