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Keywords:

  • Diaphony;
  • hybrid point set;
  • digital (t, s)-sequence;
  • lattice point set;
  • worst-case integration error MSC (2010) 11K06;
  • 11K38;
  • 11K45;
  • 65D30

Abstract

In this paper, we discuss hybrid point sets built from two of the most prominent classes of sequences used in quasi-Monte Carlo methods. We derive an existence result on point sets with low diaphony, where the components of the points involved stem from a digital (t, s)-sequence on the one hand, and from a lattice point set on the other. Moreover, we outline how the hybrid diaphony of the point sets considered in this paper relates to the worst-case integration error in suitable function spaces.