<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The LS-sequences are a parametric family of sequences of points in the unit interval. They were introduced by Carbone [4], who also proved that under an appropriate choice of the parameters L and S, such sequences are lowdiscrepancy. The aim of the present paper is to provide explicit constants in the bounds of the discrepancy of LS-sequences. Further, we generalize the construction of Carbone [4] and construct a new class of sequences of points in the unit interval, the generalized LS-sequences.</p></abstract>

The LS-sequences are a parametric family of sequences of points in the unit interval. They were introduced by Carbone [4], who also proved that under an appropriate choice of the parameters L and S, such sequences are lowdiscrepancy. The aim of the present paper is to provide explicit constants in the bounds of the discrepancy of LS-sequences. Further, we generalize the construction of Carbone [4] and construct a new class of sequences of points in the unit interval, the generalized LS-sequences.

Discrepancy of Generalized LS-Sequences

Uniform distribution theory

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

{"article-title":"Discrepancy of Generalized LS-Sequences"}

The LS-sequences are a parametric family of sequences of points in the unit interval. They were introduced by Carbone [4], who also proved that under an...

Discrepancy of Generalized LS-Sequences

Publié en ligne: 30 janv. 2018

Pages: 37 - 63

Reçu: 23 mars 2015

Accepté: 08 janv. 2017

DOI: https://doi.org/10.1515/udt-2017-0014

Mots clés
Discrepancy, LS-sequence, uniform distribution, beta-expansion

© 2018

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

Discrepancy of Generalized LS-Sequences

Publié en ligne: 30 janv. 2018

Pages: 37 - 63

Reçu: 23 mars 2015

Accepté: 08 janv. 2017

DOI: https://doi.org/10.1515/udt-2017-0014

Mots clésDiscrepancy, LS-sequence, uniform distribution, beta-expansion

© 2018

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

Mots clés
Discrepancy, LS-sequence, uniform distribution, beta-expansion