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The weighted star discrepancy is a quantitative measure for the performanceof point sets in quasi-Monte Carlo algorithms for numerical integration. Weconsider polynomial lattice point sets, whose generating vectors can beobtained by a component-by-component construction to ensure a small weightedstar discre-pancy. Our aim is to significantly reduce the construction cost ofsuch generating vectors by restricting the size of the set of polynomials fromwhich we select the components of the vectors. To gain this reduction weexploit the fact that the weights of the spaces we consider decay very fast.

A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy