Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L_p- and S_{p,q}^rB-discrepancy of (order 2) digital nets   Dick proved that all order $2$ digital nets satisfy optimal upper bounds of
the $L_2$-discrepancy. We give an alternative proof for this fact using Haar
bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds
of the $S_{p,q}^r B$-discrepancy for a certain parameter range and enlarge that
range for order $2$ digitals nets. $L_p$-, $S_{p,q}^r F$- and $S_p^r
H$-discrepancy is considered as well.

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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an