<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)

Published Online: Jan 25, 2019

Page range: 103 - 130

Received: Aug 01, 2017

Accepted: Mar 01, 2018

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

Keywords
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)

Published Online: Jan 25, 2019

Page range: 103 - 130

Received: Aug 01, 2017

Accepted: Mar 01, 2018

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

KeywordsDiscrepancy, 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.

Keywords
Discrepancy, Lower bounds, special sequences