Is there an algorithmically efficient way to compute the following value?

Define f(n, k) to be the minimum number of k-cliques to cover all edges of a complete graph of size n.

For example, f(4, 3) = 3, according to the following decomposition (0, 1, 2), (1, 2, 3), (0, 1, 3). Any edge (x, y) in the complete graph appears on the at least one of the cliques.

I want to know precise values of f on the order of f(12, 4), f(64, 16). Tried z3py solver with some naive implementations but it seems to take too long.

Are there some resources that I can learn from? Thank you.