<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.

{"article-title":{"italic":"Ls","content":["On The Classification of","-Sequences"]}}

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

Published Online: Jan 25, 2019

Page range: 83 - 92

Received: Dec 04, 2017

Accepted: Jan 23, 2018

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

Keywords
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

Published Online: Jan 25, 2019

Page range: 83 - 92

Received: Dec 04, 2017

Accepted: Jan 23, 2018

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

KeywordsLow-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.

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