Quasi-monte carlo methods in practice: quasi-monte carlo methods for simulation
Proceedings of the 35th conference on Winter simulation: driving innovation
Fast random number generators based on linear recurrences modulo 2: overview and comparison
WSC '05 Proceedings of the 37th conference on Winter simulation
A study of variance reduction techniques for American option pricing
WSC '05 Proceedings of the 37th conference on Winter simulation
Randomly shifted lattice rules for unbounded integrands
Journal of Complexity - Special issue: Information-based complexity workshops FoCM conference Santander, Spain, July 2005
Comparison of Point Sets and Sequences for Quasi-Monte Carlo and for Random Number Generation
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
The b-adic diaphony as a tool to study pseudo-randomness of nets
NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Exact sampling with highly uniform point sets
Mathematical and Computer Modelling: An International Journal
Constructions of general polynomial lattice rules based on the weighted star discrepancy
Finite Fields and Their Applications
Constructions of (t ,m,s)-nets and (t,s)-sequences
Finite Fields and Their Applications
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Lattice rules are among the best methods to estimate integrals in a large number of dimensions. They are part of the quasi-Monte Carlo set of tools. A theoretical framework for a class of lattice rules defined in a space of polynomials with coefficients in a finite field is developed in this paper. A randomized version is studied, implementations and criteria for selecting the parameters are discussed, and examples of its use as a variance reduction tool in stochastic simulation are provided. Certain types of digital net constructions, as well as point sets constructed by taking all vectors of successive output values produced by a Tausworthe random number generator, are special cases of this method.