In [1], Leonard gives a process for constructing of Zcyclic whist tournaments for
q^{2} 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 Zcyclic whist tournaments
The file provides data for quickly constructing a single Zcyclic whist tournament on
q^{2} 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, [[A_{1},B_{1}], [A_{2},B_{2}], ..., [A_{m}, B_{m}]].
Here

q is a prime congruent to 3 modulo 4;

g is an element of the multiplicative group
(Z/(q^{2}))^{×} of order (q1)/2;

the pairs [A_{i}, B_{i}] 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
[ g^{j} A_{k}, g^{j} B_{k};
g^{j} A_{k}, g^{j} B_{k}]
where all computations are done in Z/(q^{2}). Here,
1 ≤ k ≤ (q+1)/2 and 0 ≤ j < (q1)/2.
Subsequent rounds of the whist tournament come successively adding 1 to each element of the
previous round, computations again done in Z/(q^{2}).
[1] Leonard, Philip A., Some new Zcyclic whist tournaments, Utilitas Math.
49 (1996), 223232.
