Hamiltonian circuits in certain prisms

A partition of the nonzero elements of the finite abelian group $\text{Z}\text{7}\text{Z}\text{×}\text{Z}\text{7}\text{Z}$ into four sum-free sets shows that N(3,3,3,3;2) > 49. Based on a matrix technique for analyzing the structure of the two nonisomorphic 16-vertex edge-colorings nondegenerate with respect to N(3, 3, 3; 2), an involved argument proves that no 65-vertex coloring nondegenerate with respect to N(3, 3, 3, 3; 2) exists. Thus 49 < N(3,3,3,3;2) ≤ 65.