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September 2011 A lower bound on a quantity related to the quality of polynomial lattices
Peter Kritzer, Friedrich Pillichshammer
Funct. Approx. Comment. Math. 45(1): 125-137 (September 2011). DOI: 10.7169/facm/1317045237

Abstract

In this paper, we study a quantity $R_b$ which is closely related to the quality of an important subclass of digital $(t,m,s)$-nets over a finite field $\mathbb{F}_b$, namely polynomial lattices. Niederreiter has shown by an averaging argument that there always exist generators of polynomial lattices for which $R_b$ is small, establishing thereby the existence of polynomial lattices with particularly low star discrepancy. In this work, we show that this result is best possible, i.e., we prove that for all generators of polynomial lattices the quantity $R_b$ cannot go below a certain threshold.

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Peter Kritzer. Friedrich Pillichshammer. "A lower bound on a quantity related to the quality of polynomial lattices." Funct. Approx. Comment. Math. 45 (1) 125 - 137, September 2011. https://doi.org/10.7169/facm/1317045237

Information

Published: September 2011
First available in Project Euclid: 26 September 2011

zbMATH: 1247.11097
MathSciNet: MR2865418
Digital Object Identifier: 10.7169/facm/1317045237

Subjects:
Primary: 11K06
Secondary: 11T06

Rights: Copyright © 2011 Adam Mickiewicz University

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Vol.45 • No. 1 • September 2011
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