Existence of Generalized Howell designs of side n + 1 and order 3n

Abstract

Generalized Howell designs were first formulated by Deza and Vanstone in the investigation of permutation arrays. This article investigates the spectrum of generalized Howell design GHD(n+1,3n). We show that there exists a GHD(n +1,3n) for any positive integer n > 6 with at most 5 possibly exceptions for n.