Shifted lattice rules based on a general weighted discrepancy for integrals over Euclidean space (Q843126)

In the paper under review, the approximate calculation of weighted integrals over Euclidean space by using shifted rank \(-1\) lattice rules with good bounds on the general weighted star discrepancy is considered. The author firstly defines the general weighted star discrepancy \(GD^*_n\), and proves that \(GD^*_n= O(n^{-1+\delta})\) for any \(\delta> 0\), where the constant involved is independent of the dimension. Then he gives the component-by-component technique to construct the generating vector of these shifted lattice rules. Finally, the computational costs incurred by the construction are also discussed.