Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-Monte Carlo rules for numerical integration over the unit sphere
  $\mathbb{S}^2$   We study numerical integration on the unit sphere $\mathbb{S}^2 \subset
\mathbb{R}^3$ using equal weight quadrature rules, where the weights are such
that constant functions are integrated exactly.
  The quadrature points are constructed by lifting a $(0,m,2)$-net given in the
unit square $[0,1]^2$ to the sphere $\mathbb{S}^2$ by means of an area
preserving map. A similar approach has previously been suggested by Cui and
Freeden [SIAM J. Sci. Comput. 18 (1997), no. 2].
  We prove three results. The first one is that the construction is (almost)
optimal with respect to discrepancies based on spherical rectangles. Further we
prove that the point set is asymptotically uniformly distributed on
$\mathbb{S}^2$. And finally, we prove an upper bound on the spherical cap
$L_2$-discrepancy of order $N^{-1/2} (\log N)^{1/2}$ (where $N$ denotes the
number of points). This slightly improves upon the bound on the spherical cap
$L_2$-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Comm.
Pure Appl. Math. 39 (1986), 149--186]. Numerical results suggest that the
$(0,m,2)$-nets lifted to the sphere $\mathbb{S}^2$ have spherical cap
$L_2$-discrepancy converging with the optimal order of $N^{-3/4}$.

20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con