Some new Z-cyclic whist tournaments

Let p1, p2 denote primes such that p1≡1(mod 36), i=1,2. One result in this study is the formulation of a set of sufficient conditions, the satisfaction of which guarantees the existence of Z-cyclic whist tournaments when the number of players has the form 3³p1+1. By judiciously representing elements and subsets of Z3³p1p2, Z-cyclic whist tournaments for 3³p1p2+1 players are shown to be directly obtainable from the tournament on 3³p1+1 players. Data supporting the sufficient conditions is provided for all primes p1 such that 37≤p1<5000, p1≡1(mod 36).