An improved lower bound for finite additive 2-bases

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• 作者：Jukka Kohonen ^{jukka.kohonen@aalto.fi}
• 关键词：11B13
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：174
• 期：Complete
• 页码：518-524
• 全文大小：279 K
• 卷排序：174

文摘

A set of non-negative integers A is an additive 2-basis with range n  , if its sumset A+AA+A contains 0,1,…,n0,1,…,n but not n+1n+1. Explicit bases are known with arbitrarily large size |A|=k|A|=k and n/k2≥2/7>0.2857n/k2≥2/7>0.2857. We present a more general construction and improve the lower bound to 85/294>0.289185/294>0.2891.