Sets in Abelian groups with distinct sums of pairs

A subset S={s1,…,sk} of an Abelian group G is called an St-set of size k if all sums of t different elements in S are distinct. Let s(G) denote the cardinality of the largest S2-set in G. Let v(k) denote the order of the smallest Abelian group for which s(G)⩾k. In this article, bounds for s(G) are developed and v(k) is determined for k⩽15 by computing s(G) for Abelian groups of order up to 183 using exhaustive backtrack search with isomorph rejection.