Exponentially many nonisomorphic orientable triangular embeddings of K12sK12s

It was proved earlier that there are constants M  , c>0c>0 such that for every n⩾Mn⩾M (resp., every n⩾Mn⩾M, n≢0,3mod12) there are at least c2n/6c2n/6 nonisomorphic nonorientable (resp., orientable) genus embeddings of KnKn. In the present paper we show that for s⩾6s⩾6 there are at least 2s-62s-6 nonisomorphic OT-embeddings of K12sK12s. As a byproduct, we give a relatively simple method of constructing index four current graphs with current group Z12sZ12s generating orientable triangular embeddings of K12sK12s.