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A construction of higher-rank lattice rules

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  • Langtry, Timothy N.

Abstract

Lattice rules are quasi-Monte Carlo methods for numerical multiple integration that are based on the selection of an s-dimensional integration lattice. The abscissa set is the intersection of the integration lattice with the unit hypercube. It is well-known that the abscissa set of a lattice rule can be generated by a number of fixed rational vectors. In general, different sets of generators produce different integration lattices and rules, and a given rule has many different generator sets. The rank of the rule is the minimum number of generators required to span the abscissa set.

Suggested Citation

  • Langtry, Timothy N., 2001. "A construction of higher-rank lattice rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(1), pages 103-111.
    • Handle: RePEc:eee:matcom:v:55:y:2001:i:1:p:103-111
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