In 1978 Erdős asked if every sufficiently large set of points in general position in the plane contains the vertices of a convex k-gon, with the additional property that no other point of the set lies in its interior. Shortly after, Horton provided a construction—which is now called the Horton set—with no such 7-gon. In this paper we show that the Horton set of n points can be realized with integer coordinates of absolute value at most 12n12log(n/2). We also show that any set of points with integer coordinates combinatorially equivalent (with the same order type) to the Horton set contains a point with a coordinate of absolute value at least c⋅n124log(n/2), where c is a positive constant.