Generating Nonisomorphic Quadrangular Embeddings of a Complete Graph

We construct (2s)!=22slog2s−O(s) (resp. (2s−2)!=22slog2s−O(s)) index one current graphs with current group Z8s+5 such that the current graphs have different underlying graphs and generate nonisomorphic orientable (resp. nonorientable) quadrangular embeddings of the complete graph K8s+5, s≥1 (resp. s≥2).