<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri’s 80th birthday we aim to survey (some of) his contributions over the last four decades which considerably improved our understanding of one-dimensional van der Corput sequences and inspired a lot of related work. We recall and compare the different approaches in the search for generalised van der Corput sequences with low discrepancy, i.e., using a single generating permutation versus using a sequence of permutations. Throughout, we collect, sharpen and extend open questions which all stem from the extensive work of Henri and his coworkers and which will hopefully inspire more work in the future.</p></abstract>

The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the research work of Henri Faure. On the occasion of Henri’s 80th birthday we aim to survey (some of) his contributions over the last four decades which considerably improved our understanding of one-dimensional van der Corput sequences and inspired a lot of related work. We recall and compare the different approaches in the search for generalised van der Corput sequences with low discrepancy, i.e., using a single generating permutation versus using a sequence of permutations. Throughout, we collect, sharpen and extend open questions which all stem from the extensive work of Henri and his coworkers and which will hopefully inspire more work in the future.

On the Intriguing Search for Good Permutations

Uniform distribution theory

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

{"article-title":"On the Intriguing Search for Good Permutations"}

The intriguing search for permutations that generate generalised van der Corput sequences with exceptionally small discrepancy forms an important part of the...

On the Intriguing Search for Good Permutations

Published Online: Mar 27, 2020

Page range: 53 - 86

Received: Jun 20, 2018

Accepted: Jul 27, 2018

DOI: https://doi.org/10.2478/udt-2019-0005

Keywords
Van der Corput sequence, low discrepancy, permutation polynomial, Henri Faure

© 2019 Florian Pausinger, published by Sciendo

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

On the Intriguing Search for Good Permutations

Published Online: Mar 27, 2020

Page range: 53 - 86

Received: Jun 20, 2018

Accepted: Jul 27, 2018

DOI: https://doi.org/10.2478/udt-2019-0005

KeywordsVan der Corput sequence, low discrepancy, permutation polynomial, Henri Faure

© 2019 Florian Pausinger, published by Sciendo

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

Keywords
Van der Corput sequence, low discrepancy, permutation polynomial, Henri Faure