On the \(L_p\)-discrepancy of the Hammersley point set
type: Item
instance of: scholarly article
title: On the \(L_p\)-discrepancy of the Hammersley point set
zbMATH Open document ID: 1010.11043
author: Friedrich Pillichshammer
published in: Monatshefte für Mathematik
publication date: 2002-09-10T00:00:00Z
review text: For the Hammersley point set \(\mathcal H_s\) in base 2 in the unit square the \(L_p\)-discrepancy is computed as \[ \frac 1N \left(\frac {s^p}{2^{3p}}+O(s^{p-1})\right)^{1/p} \] for integers \(p\), where \(N=2^s\) is the number of points in \(\mathcal H_s\). For \(p=1,2\) the exact value is obtained. For \(p=2\) this is a new proof of a result previously established by \textit{J. H. Halton} and \textit{S. C. Zaremba} [Monatsh. Math. 73, 316-328 (1969; Zbl 0183.31401)].
Mathematics Subject Classification ID: 11K38
zbMATH DE Number: 1798920
zbMATH Keywords: Hammersley point set
zbMATH Keywords: \(L_p\)-discrepancy
MaRDI profile type: Publication
full work available at URL: s006050200034
OpenAlex ID: W2068885479
DOI: 10.1007/S006050200034
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description: scientific article; zbMATH DE number 1798920