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

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 \( p \equiv 9 \pmod{16} \). It is shown here that their methodology can be generalized completely to deal with primes of the form \( p \equiv (2^k + 1) \pmod{2^{k+1}} \), \( k \geq 4 \).