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In this paper, we study an efficient algorithm for constructing point setsunderlying quasi-Monte Carlo integration rules for weighted Korobov classes.The algorithm presented is a reduced fast component-by-component digit-by-digit(CBC-DBD) algorithm, which useful for to situations where the weights in thefunction space show a sufficiently fast decay. The advantage of the algorithmpresented here is that the computational effort can be independent of thedimension of the integration problem to be treated if suitable assumptions onthe integrand are met. The new reduced CBC-DBD algorithm is designed to workfor the construction of lattice point sets, and the corresponding integrationrules (so-called lattice rules) can be used to treat functions in differentkinds of function spaces. We show that the integration rules constructed by ouralgorithm satisfy error bounds of almost optimal convergence order.Furthermore, we give details on an efficient implementation such that we obtaina considerable speed-up of a previously known CBC-DBD algorithm that has beenstudied before. This improvement is illustrated by numerical results.

On a reduced digit-by-digit component-by-component construction of lattice point sets