A Note on a Pair of Orthogonal Orthomorphisms of Cyclic Groups

By giving previously unknown a pair of orthogonal orthomorphisms of cyclic groups of order 18 t + 9 for any positive integer t , we complete the existence spectrum of a pair of orthogonal orthomorphisms of cyclic groups. As a corollary, we complete the existence spectrum of a difference matrix with four rows over any finite abelian group.