On the exact t-value of Niederreiter and Sobol' sequences

Authors:
Josef Dick;Harald Niederreiter
Affiliations:
School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia;Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore
Venue:
Journal of Complexity
Year:
2008

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Abstract

This paper studies several well-known families of (t,s)-sequences. First we determine the exact t-value of Niederreiter sequences. Then we analyze the exact t-value of generalized Niederreiter sequences and we show that, for a range of dimensions of practical interest, Niederreiter-Xing sequences are demonstrably better than Sobol' sequences in terms of the exact t-value. Previously, such a conclusion was not possible since only upper bounds on the exact t-value of these sequences and a general lower bound for all (t,s)-sequences were available.