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A lower bound on the star discrepancy of generalized Halton sequences in rational bases


Author: Roswitha Hofer
Journal: Proc. Amer. Math. Soc. 147 (2019), 4655-4664
MSC (2010): Primary 11K31, 11K38
DOI: https://doi.org/10.1090/proc/14596
Published electronically: May 17, 2019
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Abstract: In this paper we extend a result of Levin, who proved a lower bound on the star discrepancy of generalized Halton sequences in positive integer bases, to rational bases.


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Additional Information

Roswitha Hofer
Affiliation: Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz, Altenbergerstr. 69, 4040 Linz, Austria
Email: roswitha.hofer@jku.at

DOI: https://doi.org/10.1090/proc/14596
Keywords: Halton sequences, discrepancy, lower bounds
Received by editor(s): October 30, 2018
Received by editor(s) in revised form: February 19, 2019
Published electronically: May 17, 2019
Additional Notes: The author was supported by the Austrian Science Fund (FWF): Project F5505-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2019 American Mathematical Society