The existence of good extensible rank-1 lattices

Fred J. Hickernell*, Harald Niederreiter

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

57 Citations (Scopus)


Extensible integration lattices have the attractive property that the number of points in the node set may be increased while retaining the existing points. It is shown here that there exist generating vectors, h, for extensible rank-1 lattices such that for n = b, b2, ... points and dimensions s = 1, 2, ... the figures of merit Rα, Pα, and discrepancy are all small. The upper bounds obtained on these figures of merit for extensible lattices are some power of log n worse than the best upper bounds for lattices where h is allowed to vary with n and s.

Original languageEnglish
Pages (from-to)286-300
Number of pages15
JournalJournal of Complexity
Issue number3
Publication statusPublished - Jun 2003
Externally publishedYes

Scopus Subject Areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

User-Defined Keywords

  • Discrepancy
  • Extensible lattices
  • Figures of merit
  • Lattice rules
  • Quasi-Monte Carlo integration


Dive into the research topics of 'The existence of good extensible rank-1 lattices'. Together they form a unique fingerprint.

Cite this