On an example of finite hybrid quasi-Monte Carlo point sets

Abstract

In this paper, we consider finite hybrid point sets in the unit cube. The components of these stem from two well known types of low discrepancy point sets, namely Hammersley point sets on the one hand, and lattice point sets in the sense of Korobov and Hlawka on the other hand. As a quality measure, we consider the star discrepancy, which gives information about the quality of distribution of finite or infinite sequences. We present existence results for finite hybrid point sets with low discrepancy. Thereby, we make analogous results for infinite sequences more explicit in the sense that, theoretically, it is now possible to find such finite hybrid low discrepancy point sets.