An improved lower bound for finite additive 2-bases

TL;DR

This paper improves the lower bound on the range of finite additive 2-bases, demonstrating a more general construction that slightly increases the known ratio of range to the square of the size.

Contribution

It introduces a more general construction method that improves the lower bound for the range of finite additive 2-bases.

Findings

Lower bound improved to 85/294 (~0.2891)

Explicit bases with large size and known ratios

Enhanced understanding of additive 2-bases range limits

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 $85/294 > 0.2891$.