A construction for sets of integers with distinct subset sums

Abstract

A set S of positive integers has distinct subset sums if there are 2 |S| distinct elements of the set {∑x∈X x : X ⊂ S}. Let f(n) = min{max S : |S| = n and S has distinct subset sums}. Erdos conjectured f(n) ≥ c2n for some constant c. We give a construction that yields f(n) < 0.22002 · 2n for n sufficiently large. This now stands as the best known upper bound on f(n).