Perfect 2-colorings of Hamming graphs

We consider the problem of existence of perfect 2-colorings (equitable 2-partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs and colorings that are necessary for their existence. Next we observe known constructions of perfect colorings and propose some new ones giving new parameters. At last, we deduce which parameters of colorings are covered by these constructions and give tables of admissible parameters of 2-colorings in Hamming graphs (Formula presented.) for small (Formula presented.) and (Formula presented.). Using the connection with perfect colorings, we construct an orthogonal array OA(2048, 7, 4, 5).