In , Leonard gives a process for constructing of Z-cyclic whist tournaments for
q2 players, where q is a prime congruent to 3 modulo 4. The construction
seems to work for all such q > 7, but this is not proven. Here we provide data
from computations for 7 < q < 5000 (range extended 11/06):
Data file of Z-cyclic whist tournaments
The file provides data for quickly constructing a single Z-cyclic whist tournament on
q2 players for each prime considered. It contains a list of the form
[data for prime 1, data for prime 2, ...],
where each term of the list has the form
[q, g, [[A1,B1], [A2,B2], ..., [Am, Bm]].
q is a prime congruent to 3 modulo 4;
g is an element of the multiplicative group
(Z/(q2))× of order (q-1)/2;
the pairs [Ai, Bi] provide the needed data to write
down the tables of the tournament. The number of these is
m = (q+1)/2.
Given this information, one constructs the initial round tables of the form
[ gj Ak, gj Bk;
-gj Ak, -gj Bk]
where all computations are done in Z/(q2). Here,
1 ≤ k ≤ (q+1)/2 and 0 ≤ j < (q-1)/2.
Subsequent rounds of the whist tournament come successively adding 1 to each element of the
previous round, computations again done in Z/(q2).
 Leonard, Philip A., Some new Z-cyclic whist tournaments, Utilitas Math.
49 (1996), 223-232.