On Proinov’s Lower Bound for the Diaphony

Nathan Kirk

doi:10.2478/udt-2020-0010

On Proinov’s Lower Bound for the Diaphony

Nathan Kirk

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

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Abstract

In 1986, Proinov published an explicit lower bound for the diaphony of both finite and infinite sequences of points in the d-dimensional unit cube. To the best of our knowledge, the proofs of these results were so far only available in a monograph of Proinov written in Bulgarian. The first contribution of our paper is to give a self contained version of Proinov's proof in English. Along the way, we improve the asymptotic constants using recent and corrected results of Hinrichs and Markhasin. Finally, as a main result, we use the method of Proinov to derive an explicit lower bound for the dyadic diaphony of finite and infinite sequences in a similar fashion.

Original language	English
Article number	4
Pages (from-to)	39-72
Number of pages	34
Journal	Uniform Distribution Theory
Volume	15
Issue number	2
DOIs	https://doi.org/10.2478/udt-2020-0010
Publication status	Published - 25 Dec 2020

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10.2478/udt-2020-0010Licence: CC BY-NC-ND

On Proinov’s Lower Bound for the Diaphony
© 2020 BOKU-University of Natural Resources and Life Sciences and Mathematical Institute, Slovak Academy of Sciences. This is an open access article published under a Creative Commons Attribution-NonCommercial-NoDerivs License (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits distribution and reproduction for non-commercial purposes, provided the author and source are cited.
Final published version, 466 KBLicence: CC BY-NC-ND

Several problems in discrepancy theory: lower bounds and stratified sampling
Kirk, N. (Author), Barnes, D. (Supervisor), Lin, Y.-F. (Supervisor) & Pausinger, F. (Supervisor), Jul 2023
Student thesis: Doctoral Thesis › Doctor of Philosophy

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On Proinov’s Lower Bound for the Diaphony

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Several problems in discrepancy theory: lower bounds and stratified sampling

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