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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 special choice 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 whicharXiv:1501.07073v1 fatcat:pb364zbgkrgcpoco3dtlpndtsm