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Claim. G. Yu, A new upper bound for finite additive $h$-bases, J. Number Theory 156 (2015), 95--104. For $h=2$, with $n(k)$ the maximal range of an additive $2$-basis of size $k$, the paper proves

$$\limsup_{k\to\infty}\frac{n(k)}{k^2}\le0.4585,$$

the statement as J. Kohonen, An improved lower bound for finite additive 2-bases, J. Number Theory 174 (2017), p. 1, quotes it; the paper itself is not held, and its bounds for other $h$ are not recorded here. In the notation of Problem 791, $g(n)=\min\{k:n(k)\ge n\}$ and $g(n)\to\infty$; if $n(k)\le(0.4585+\varepsilon)k^2$ for all large $k$, then for large $n$ $n\le n(g(n))\le(0.4585+\varepsilon)g(n)^2$, so

$$g(n)^2\ge\Bigl(\frac1{0.4585}-o(1)\Bigr)n,\qquad\frac1{0.4585}=2.1810\ldots,$$

the lower bound the site's commentary gives as $2.181\cdots$.

Covers. The lower bound $g(n)^2\ge(1/0.4585-o(1))n$ for the estimate of $g(n)$. Not covered: the value of $\lim g(n)^2/n$, or whether it exists.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper is published in the Journal of Number Theory (Crossref: 2015-11), which dates this page. The site's curator, Thomas F. Bloom, cites the bound in the problem's commentary, but the site labels the problem OPEN, so the citation is not listed as reviewed. The proof is not reviewed in this corpus.