An improved lower bound for finite additive 2-bases

Abstract

A set of non-negative integers A is an additive 2-basis with range n, if its sumset A+A contains 0, 1, ..., n but not n+1. Explicit bases are known with arbitrarily large size |A|=k and $n/k^2\ge 2/7>0.2857$. We present a more general construction and improve the lower bound to $85/294>0.2891$.

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