Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the inverse of the star-discrepancy   The inverse of the star-discrepancy $N^*(d,\ve)$ denotes the smallest
possible cardinality of a set of points in $[0,1]^d$ achieving a
star-discrepancy of at most $\ve$. By a result of Heinrich, Novak, Wasilkowski
and Wo{\'z}niakowski, $$ N^*(d,\ve) \leq c_{\textup{abs}} d \ve^{-2}. $$ Here
the dependence on the dimension $d$ is optimal, while the precise dependence on
$\ve$ is an open problem. In the present paper we prove that $$ N^*(d,\ve) \leq
c_{\textup{abs}} d \ve^{-3/2} (\log (\ve^{-1}))^{1/2}. $$ This is a surprising
result, which disproves a conjecture of Novak and Wo{\'z}niakowski.

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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: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: eess