On a Reduced Component-by-Component Digit-by-Digit Construction of Lattice Point Sets

Abstract In this paper, we study an efficient algorithm for constructing point sets underlying quasi-Monte Carlo integration rules weighted Korobov classes. The presented is a reduced fast component-by-component digit-by-digit (CBC-DBD) algorithm, which useful situations where the weights in function space show sufficiently decay. advantage of here that computational effort can be independent dimension problem to treated if suitable assumptions on integrand are met. By considering construction, allow less precise with respect number bits those components considered important. new CBC-DBD designed work construction lattice sets, and corresponding (so-called rules) used treat functions different kinds spaces. We constructed by our satisfy error bounds almost optimal convergence order. Furthermore, give details implementation such obtain considerable speed-up previously known has been studied paper Digit-by-digit constructions periodic unknown smoothness Ebert, Kritzer, Nuyens, Osisiogu, published Journal Complexity 2021. This improvement illustrated numerical results.