Let's consider subsets of the set $\{1,\dots,n\}$ which consist of $m$ elements. I wonder, what is the maximal number of such subsets such that cardinality of intersection of any two of them isn't equal to $k$. Let's call $f(n,m,k)$.
I considered some cases and proved, for instance, the equality $f(4n,3,1)=4n$.
Is there a general way to compute values of $f$?