Let Kq(n,R) denote the minimum number of codewords in any q-ary code of length n and covering radius R. We collect lower and upper bounds for Kq(n,R) where 6 ? q ? 21 and R ? 3. For q ? 10, we consider lengths n ? 10, and for q ? 11, we consider n ? 8. This extends earlier results, which have been tabulated for 2 ? q ? 5. We survey known bounds and obtain some new results as well, also for s-surjective codes, which are closely related to covering codes and utilized in some of the constructions.