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In this paper, we study an efficient algorithm for constructing node sets ofhigh-quality quasi-Monte Carlo integration rules for weighted Korobov, Walsh,and Sobolev spaces. The algorithm presented is a reduced fast successivecoordinate search (SCS) algorithm, which is adapted to situations where theweights in the function space show a sufficiently fast decay. The new SCSalgorithm is designed to work for the construction of lattice points, and, in amodified version, for polynomial lattice points, and the correspondingintegration rules can be used to treat functions in different kinds of functionspaces. We show that the integration rules constructed by our algorithmssatisfy error bounds of optimal convergence order. Furthermore, we give detailson efficient implementation such that we obtain a considerable speed-up ofpreviously known SCS algorithms. This improvement is illustrated by numericalresults. The speed-up obtained by our results may be of particular interest inthe context of QMC for PDEs with random coefficients, where both the dimensionand the required numberof points are usually very large. Furthermore, our maintheorems yield previously unknown generalizations of earlier results.

Constructing lattice points for numerical integration by a reduced fast successive coordinate search algorithm