A van der Corput-type algorithm for LS-sequences of points

Abstract

In this paper we associate to any $LS$-sequence of partitions ${\rho }_{L,S}^n$ the corresponding $LS$-sequence of points ${\xi }_{L,S}^n$ obtained reordering the points of each partition with an explicit algorithm. The procedure begins with the representation in base $L+S$ of natural numbers, $[n{]}_{L+S}$, and ends with the $LS$-radical inverse function ${\varphi }_{L,S}$, introduced ad hoc, evaluated at an appropriate subsequence of natural numbers depending on $L$ and $S$. This construction is deeply related to the geometric representation of the points of ${\xi }_{L,S}^n$ by suitable affine functions and reminds the van der Corput sequences in base $b$. Keywords: Uniform distribution, sequences of partitions, van der Corput sequences, discrepancy.

This paper is withdrawn as it is replaced by "How to construct generalized van der Corput sequences" - arXiv:1304.5083. The latter paper coincides with the former, up to minor changes, an improvement of the references, and (hopefully) a more clear presentation. The new title would better show the aim of the paper, which has been submitted in this final form

Cited by in corpus (2)

• $LS$-sequences of points in the unit square
• $LS$-successioni di punti nel quadrato