Summary: A subset S of a finite Abelian group G is said to be a sum cover of G if every element of G can be expressed as the sum of two not necessarily distinct elements in S , a strict sum cover of G if every element of G can be expressed as the sum of two distinct elements in S , and a difference cover of G if every element of G can be expressed as the difference of two elements in S . For each type of cover, we determine for small k the largest Abelian group for which a k -element cover exists. For this purpose we compute a minimum sum cover, a minimum strict sum cover, and a minimum difference cover for Abelian groups of order up to 85, 90, and 127, respectively, by a backtrack search with isomorph rejection.

05B40, 20K01

additive base, backtrack search, difference set, covering