In this paper we consider a control system of type x+ = x + u, wnere the u take values in a set of 2m + 1 integer numbers, symmetric with respect to 0. and analyse the reachable set after K steps. Our aim is to find a set of m input values such that the reachable set after K steps contains an interval of integers [-N,.,., N] with N as large as possible. For m = 2 and 3, we completely solve the problem and characterize the metric associated to this quantized control system. Copyright © 2004 IFAC.