An improved lower bound for finite additive 2-bases

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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/k²≥2/7>0.2857. We present a more general construction and improve the lower bound to 85/294>0.2891.
Original languageEnglish
Pages (from-to)518–524
JournalJournal of Number Theory
Volume174
DOIs
Publication statusPublished - May 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Finite additive basis
  • Additive number theory

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