New classes of complete balanced Howell rotations

Complete balanced Howell rotations (CBHR) owe their origins to duplicate bridge tournaments but have since been shown to possess of deep combinatorial properties. They include many other combinatorial designs as special cases, such as: balanced Howell rotations, weak complete balanced Howell rotations, Room squares, Howell designs, and a class of balanced incomplete block designs.All known CBHR's are for n partnerships such that n = 2^t(p^r + 1), where p^r is an odd prime power and t a natural number. In most cases, p^r ≡ 3(mod 4) is also assumed. Berlekamp and Hwang gave constructions of CBHR's for each such n > 3 with t = 0; Schellenberg gave constructions for each such n with t = 1. In this paper, we construct CBHR for each such n with t arbitrary.