Vandermonde nets

Roswitha Hofer, and Harald Niederreiter. "Vandermonde nets." Acta Arithmetica 163.2 (2014): 145-160. <http://eudml.org/doc/286076>.

@article{RoswithaHofer2014,
abstract = {The second-named author recently suggested identifying the generating matrices of a digital (t,m,s)-net over the finite field $_\{q\}$ with an s × m matrix C over $_\{q^\{m\}\}$. More exactly, the entries of C are determined by interpreting the rows of the generating matrices as elements of $_\{q^\{m\}\}$. 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 $_\{q\}$ 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.},
author = {Roswitha Hofer, Harald Niederreiter},
journal = {Acta Arithmetica},
keywords = {digital net; discrepancy},
language = {eng},
number = {2},
pages = {145-160},
title = {Vandermonde nets},
url = {http://eudml.org/doc/286076},
volume = {163},
year = {2014},
}

TY - JOUR
AU - Roswitha Hofer
AU - Harald Niederreiter
TI - Vandermonde nets
JO - Acta Arithmetica
PY - 2014
VL - 163
IS - 2
SP - 145
EP - 160
AB - The second-named author recently suggested identifying the generating matrices of a digital (t,m,s)-net over the finite field $_{q}$ with an s × m matrix C over $_{q^{m}}$. More exactly, the entries of C are determined by interpreting the rows of the generating matrices as elements of $_{q^{m}}$. 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 $_{q}$ 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.
LA - eng
KW - digital net; discrepancy
UR - http://eudml.org/doc/286076
ER -