On the Construction of Directed Triplewhist Tournaments.

We show that, for all primes \(p \equiv 1 \pmod{4}\), \(29 \leq p < 10,000\), \(p \neq 97, 193, 257, 449, 641, 769, 1153, 1409, 7681\), there exist \({Z}\)-cyclic triplewhist tournaments on \(p\) elements which are also Mendelsohn designs. We also show that such designs exist on \(v\) elements whenever \(v\) is a product of such primes \(p\).