Correction of the Lusztig-Williamson Billiards Conjecture

A new algorithm allows us to calculate many new tilting characters for $S{L}_3$, $S{P}_4$, $G_2$, $S{L}_4$ and potentially many other groups. These calculations show that the Lusztig-Williamson Billiards Conjecture needs to be corrected. In this paper we present the new results calculated for $S{L}_3$ and a correction of the conjecture.