  There are many papers studying properties of point sets in the Euclidean
space $\mathbb{E}^m$ or on integer grids $\mathbb{Z}^m$, with pairwise integral
or rational distances. In this article we consider the distances or coordinates
of the point sets which instead of being integers are elements of $\mathbb{Z} /
\mathbb{Z}n$, and study the properties of the resulting combinatorial
structures.
