Joe, StephenSinescu, Vasile2009-02-112009-02-112008Sinescu, V. & Joe, S.(2008). Good lattice rules with a composite number of points based on the product weighted star discrepancy. In H. Niederreiter & D. Talay (Eds), Monte Carlo and Quasi-Monte Carlo Methods 2006(pp. 645-658). Berlin, Germany: Springer.https://hdl.handle.net/10289/2004Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend these results to the non-prime case. We show that if the weights are summable, there exist lattice rules whose weighted star discrepancy is O(n−1+δ), for any δ > 0, with the implied constant independent of the dimension and the number of lattice points, but dependent on δ and the weights. Then we show that the generating vector of such a rule can be constructed using a component-by-component (CBC) technique. The cost of the CBC construction is analysed in the final part of the paper.application/pdfenThis is an author’s version of article published in the book: Monte Carlo and Quasi-Monte Carlo Methods 2006.mathematicsrank-1 lattice rulesweighted start discrepancycomponent-by-component constructionChapter in Book10.1007/978-3-540-74496-2_39