<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The goal of this overview article is to give a tangible presentation of the breakthrough works in discrepancy theory [3, 5] by M. B. Levin. These works provide proofs for the exact lower discrepancy bounds of Halton’s sequence and a certain class of (<italic>t, s</italic>)-sequences. Our survey aims at highlighting the major ideas of the proofs and we discuss further implications of the employed methods. Moreover, we derive extensions of Levin’s results.</p></abstract>

The goal of this overview article is to give a tangible presentation of the breakthrough works in discrepancy theory [3, 5] by M. B. Levin. These works provide proofs for the exact lower discrepancy bounds of Halton’s sequence and a certain class of (t, s)-sequences. Our survey aims at highlighting the major ideas of the proofs and we discuss further implications of the employed methods. Moreover, we derive extensions of Levin’s results.

On M. B. Levin’s Proofs for The Exact Lower Discrepancy Bounds of Special Sequences and Point Sets (A Survey)

Uniform distribution theory

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

The goal of this overview article is to give a tangible presentation of the breakthrough works in discrepancy theory [3, 5] by M. B. Levin. These works provide...

On M. B. Levin’s Proofs for The Exact Lower Discrepancy Bounds of Special Sequences and Point Sets (A Survey)

Publié en ligne: 25 janv. 2019

Pages: 103 - 130

Reçu: 01 août 2017

Accepté: 01 mars 2018

DOI: https://doi.org/10.2478/udt-2018-0014

Mots clés
Discrepancy, Lower bounds, special sequences

© 2018 Lisa Kaltenböck et al., published by Sciendo

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

On M. B. Levin’s Proofs for The Exact Lower Discrepancy Bounds of Special Sequences and Point Sets (A Survey)

Publié en ligne: 25 janv. 2019

Pages: 103 - 130

Reçu: 01 août 2017

Accepté: 01 mars 2018

DOI: https://doi.org/10.2478/udt-2018-0014

Mots clésDiscrepancy, Lower bounds, special sequences

© 2018 Lisa Kaltenböck et al., published by Sciendo

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

Mots clés
Discrepancy, Lower bounds, special sequences