The problem of finding the domination number of Hamming graph $H(3, 2n)$ ($n$ is an integer) was given as a homework for my discrete math class. I didn't manage to solve the question. But later the solution was given to every students and the answer was $n^2/2$.

And now I have a question if there is any generalization of this problem. What kind of Hamming graphs $H(p, q)$ have exact and known domination number?