<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper addresses the question whether the <italic>LS</italic>-sequences constructed in [Car12] yield indeed a new family of low-discrepancy sequences. While it is well known that the case <italic>S</italic> = 0 corresponds to van der Corput sequences, we prove here that the case <italic>S</italic> = 1 can be traced back to symmetrized Kronecker sequences and moreover that for <italic>S ≥</italic> 2 none of these two types occurs anymore. In addition, our approach allows for an improved discrepancy bound for <italic>S</italic> = 1 and <italic>L</italic> arbitrary.</p></abstract>

This paper addresses the question whether the LS-sequences constructed in [Car12] yield indeed a new family of low-discrepancy sequences. While it is well known that the case S = 0 corresponds to van der Corput sequences, we prove here that the case S = 1 can be traced back to symmetrized Kronecker sequences and moreover that for S ≥ 2 none of these two types occurs anymore. In addition, our approach allows for an improved discrepancy bound for S = 1 and L arbitrary.

On The Classification of <italic>Ls</italic>-Sequences

Hochschule Ruhr West, Mülheim an der Ruhr

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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This paper addresses the question whether the LS-sequences constructed in [Car12] yield indeed a new family of low-discrepancy sequences. While it is well...

On The Classification of Ls-Sequences

Online veröffentlicht: 25. Jan. 2019

Seitenbereich: 83 - 92

Eingereicht: 04. Dez. 2017

Akzeptiert: 23. Jan. 2018

DOI: https://doi.org/10.2478/udt-2018-0012

Schlüsselwörter
Low-discrepancy, LS-sequences, Kronecker-sequences, classification, uniform distribution

© 2018 Christian Weiss, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

On The Classification of Ls-Sequences

Online veröffentlicht: 25. Jan. 2019

Seitenbereich: 83 - 92

Eingereicht: 04. Dez. 2017

Akzeptiert: 23. Jan. 2018

DOI: https://doi.org/10.2478/udt-2018-0012

SchlüsselwörterLow-discrepancy, LS-sequences, Kronecker-sequences, classification, uniform distribution

© 2018 Christian Weiss, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schlüsselwörter
Low-discrepancy, LS-sequences, Kronecker-sequences, classification, uniform distribution