Ovals in $${\mathbb {Z}}^2_{2p}$$

Abstract

By an oval in $${\mathbb {Z}}^2_{2p},$$ Z 2 p 2 , p odd prime, we mean a set of $$2p+2$$ 2 p + 2 points, such that no three of them are on a line. It is shown that ovals in $${\mathbb {Z}}^2_{2p}$$ Z 2 p 2 only exist for $$p=3,5$$ p = 3 , 5 and they are unique up to an isomorphism.