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Constructing Sobol' sequences with better two-dimensional projections

Abstract
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.
Type
Journal Article
Type of thesis
Series
Citation
Joe, S. & Kuo, F.Y. (2008). Constructing Sobol' sequences with better two-dimensional projections. SIAM Journal on Scientific Computing, 30(5), 2635-2654.
Date
2008-08
Publisher
Society for Industrial and Applied Mathematics
Degree
Supervisors
Rights
This article is published in the SIAM Journal on Scientific Computing. Copyright © by SIAM.