  In this paper we study hyperuniformity on flat tori. Hyperuniform point sets
on the unit sphere have been studied by J.~Brauchart, P.~Grabner, W.~Kusner and
J.~Ziefle. It is shown that point sets which are hyperuniform for large balls,
small balls or balls of threshold order on the flat tori are uniformly
distributed. Moreover, it is also shown that QMC--designs sequences for Sobolev
classes, probabilistic point sets (with respect to jittered samplings) and some
determinantal point process are hyperuniform.
