Balanced Howell rotations of the twin prime power type

Abstract

We prove by construction that a balanced Howell rotation for n n players always exists if n = p r q s n = {p^r}{q^s} where p p and q ≠ 3 q \ne 3 are primes and q s = p r + 2 {q^s} = {p^r} + 2 . This generalizes a much weaker previous result. The construction uses properties of a Galois domain which is a direct sum of two Galois fields.