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CONSTRUCTING SOBOL' SEQUENCES WITH BETTER TWO-DIMENSIONAL PROJECTIONS
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DOI：10.1137/070709359.png)
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Direction numbers for generating Sobol' sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 ( 2003), pp. 49-57]. However, these Sobol' sequences may have poor two-dimensional projections. Here we provide a new set of direction numbers alleviating this problem. These are obtained by treating Sobol' sequences in d dimensions as (t, d)-sequences and then optimizing the t-values of the two-dimensional projections. Our target dimension is 21201.
Keyword:
Sobol' sequences
two-dimensional projections
digital nets and sequences
numerical integration
quasi-Monte Carlo methods
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2.6
论文数:
5.1K
被引数:
1.8W
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