A note on the no-three-in-line problem on a torus
  In this paper we show that at most $2 \gcd(m,n)$ points can be placed with no three in a line on an $m\times n$ discrete torus. In the situation when $\gcd(m,n)$ is a prime, we completely solve the problem. 
Zofia St\c{e}pie\'n, Aleksander Misiak, Alicja Szymaszkiewicz, Lucjan   Szymaszkiewicz, Maciej Zwierzchowski
math.CO