Abstract
We observe that the time required to compute the star discrepancy of a sequence of points in a multidimensional unit cube is prohibitive and that the best known upper bounds for the star discrepancy of (t,s)-sequences and (t,m,s)-nets are useful only for sample sizes that grow exponentially with the dimension s. Then, an algorithm to compute upper bounds for the star discrepancy of an arbitrary set of n points in the s-dimensional unit cube is proposed. For an integer k≥1, this algorithm computes in O(nslogk+2s k s) time and O(k s) space a bound that is no better than a function depending on s and k. As an application, we give improved upper bounds for the star discrepancy of some Faure (0,m,s)-nets for s∈{7,…,20}.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received April 20, 1999; revised April 26, 2000
Rights and permissions
About this article
Cite this article
Thiémard, E. Computing Bounds for the Star Discrepancy. Computing 65, 169–186 (2000). https://doi.org/10.1007/s006070070018
Issue Date:
DOI: https://doi.org/10.1007/s006070070018