Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved Lower Bound for Difference Bases   A difference basis with respect to $n$ is a subset $A \subseteq \mathbb{Z}$
such that $A - A \supseteq \{1, \ldots, n\}$. R\'{e}dei and R\'{e}nyi showed
that the minimum size of a difference basis with respect to $n$ is
$(c+o(1))\sqrt{n}$ for some positive constant $c$. The best previously known
lower bound on $c$ is $c \geqslant 1.5602\ldots$, which was obtained by Leech
using a version of an earlier argument due to R\'{e}dei and R\'{e}nyi. In this
note we use Fourier-analytic tools to show that the Leech--R\'{e}dei--R\'{e}nyi
lower bound is not sharp.

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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org