Existence of directed triplewhist tournaments with the three person property 3PDTWh(v)3PDTWh(v)

A directed triplewhist tournament on vv players, briefly DTWh(v)DTWh(v), 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(v)3PDTWh(v). In this paper, we show that a 3PDTWh(v)3PDTWh(v) exists whenever v>17v>17 and v≡1(mod4) with few possible exceptions.