Reduced Fast Component-by-Component Construction of Lattice Point Sets With Small Weighted Star Discrepancy

The weighted star discrepancy of point sets appears in the weighted Koksma-Hlawka inequality and thus is a measure for the quality of point sets with respect to their performance in quasi-Monte Carlo algorithms. A specific selection of point sets are lattice point sets whose generating vector can be obtained one component at a time such that the resulting lattice point set has a small weighted star discrepancy. In this paper we consider a reduced fast component-by-component algorithm which significantly reduces the construction cost for such generating vectors pro- vided that the weights decrease fast enough.