On the Construction of Directed Triplewhist Tournaments.

Abstract

We show that, for all primes $p\equiv 1(\mathrm{mod}4)$, $29\le p<10,000$, $p\ne 97,193,257,449,641,769,1153,1409,7681$, 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 $p$.