Existence of Z-cyclic 3PDTWh(p) for Prime p ≡ 1 (mod 4)

Abstract

A directed triplewhist tournament on p players over Z p is said to have the three-person property if no two games in the tournament have three common players. We briefly denote such a design as a 3PDTWh( p). In this paper, we investigate the existence of a Z-cyclic 3PDTWh( p) for any prime p ≡ 1 (mod 4) and show that such a design exists whenever p ≡ 5, 9, 13 (mod 16) and p ≥ 29. This result is obtained by applying Weil's theorem. In addition, we also prove that a Z-cyclic 3PDTWh( p) exists whenever p ≡ 1 (mod 16) and p < 10,000 except possibly for p = 257,769.

The Researches and Analysis on Lakes Water Quality of the Guangzhou Higher Education Mega Center

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