Vandermonde nets

• Autorzy: Roswitha Hofer , Harald Niederreiter
• Języki publikacji: EN

Abstrakty

EN

The second-named author recently suggested identifying the generating matrices of a digital (t,m,s)-net over the finite field $𝔽_{q}$ with an s × m matrix C over $𝔽_{q^{m}}$. More exactly, the entries of C are determined by interpreting the rows of the generating matrices as elements of $𝔽_{q^{m}}$. This paper introduces so-called Vandermonde nets, which correspond to Vandermonde-type matrices C, and discusses the quality parameter and the discrepancy of such nets. The methods that have been successfully used for the investigation of polynomial lattice point sets and hyperplane nets are applied to this new class of digital nets. In this way, existence results for small quality parameters and good discrepancy bounds are obtained. Furthermore, a first step towards component-by-component constructions is made. A novelty of this new class of nets is that explicit constructions of Vandermonde nets over $𝔽_{q}$ in dimensions s ≤ q + 1 with best possible quality parameter can be given. So far, good explicit constructions of the competing polynomial lattice point sets are known only in dimensions s ≤ 2.

Kategorie tematyczne

• 11K38: Irregularities of distribution, discrepancy
• 11K31: Special sequences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 163
• Numer: 2
• Strony: 145-160

Daty

wydano

2014

Twórcy

autor

Roswitha Hofer

• Institute of Financial Mathematics, Johannes Kepler University Linz, Altenbergerstr. 69, A-4040 Linz, Austria

autor

Harald Niederreiter

• Johann Radon Institute for, Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, A-4040 Linz, Austria
• Department of Mathematics, University of Salzburg, Hellbrunnerstr. 34, A-5020 Salzburg, Austria

Identyfikatory

DOI

10.4064/aa163-2-5