×

On the \(L_p\)-discrepancy of the Hammersley point set. (English) Zbl 1010.11043

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 J. H. Halton and S. C. Zaremba [Monatsh. Math. 73, 316-328 (1969; Zbl 0183.31401)].

MSC:

11K38 Irregularities of distribution, discrepancy

Citations:

Zbl 0183.31401
PDF BibTeX XML Cite
Full Text: DOI