Exponentially many nonisomorphic genus embeddings of Kn,mKn,m

We prove that for every n,m≥6n,m≥6, the complete bipartite graph Kn,mKn,m has at least 18nm2⌊(n−1)/3⌋⌊(m−2)/4⌋ nonisomorphic orientable as well as nonorientable genus embeddings.