The problem of dimensionality in stratified sampling
Management Science
Implementation and tests of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Polynomial arithmetic analogue of Halton sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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One of the most recent constructions of quasi-random sequences is due to Niederreiter (1988). These sequences, which possess the lowest known discrepancy of all such sequences, have not yet been implemented as practical computer code. In this paper we gather together relevant results and theorems presented by Niederreiter (1988) to produce a concrete construction of such a sequence. An algorithm and practical routines for the generation of the sequence are presented, together with an unusual practical application from the area of discrete event simulation.We consider the estimation of daily gas demand and conclude that significant gains can be made by selecting a quasi-random sequence in preference to the traditional approach of using crude Monte Carlo.The Sobol' (1967) and Faure (1982) sequences have played an important role in the development of this, the most recent sequence. They have only marginally higher discrepancies, and so for comparison simulation results are also included for these sequences.