A Construction for Sets of Integers with Distinct Subset Sums

@article{Bohman1998ACF,
title={A Construction for Sets of Integers with Distinct Subset Sums},
author={Tom Bohman},
journal={Electr. J. Comb.},
year={1998},
volume={5}
}

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}. Erdős 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).