A Generalization of the Anderson – Ellison Methodology for $Z$-cyclic DTWh(p) and OTWh(p)

Abstract

I. Anderson and L. Ellison [7] demonstrated the existence of $Z$-cyclic Directed Triplewhist Tournament Designs and $Z$-cyclic Ordered Triplewhist Tournament Designs for all primes $p\equiv 9(\mathrm{mod}16)$. It is shown here that their methodology can be generalized completely to deal with primes of the form $p\equiv (2^k+1)(\mathrm{mod}{2}^{k+1})$, $k\ge 4$.