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Displaying similar documents to “Estimation of the integral modulus of smoothness of an even function of several variables with quasiconvex Fourier coefficients.”

L 2 discrepancy of generalized Zaremba point sets

Henri Faure, Friedrich Pillichshammer (2011)

Journal de Théorie des Nombres de Bordeaux

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We give an exact formula for the L 2 discrepancy of a class of generalized two-dimensional Hammersley point sets in base b , namely generalized Zaremba point sets. These point sets are digitally shifted Hammersley point sets with an arbitrary number of different digital shifts in base b . The Zaremba point set introduced by White in 1975 is the special case where the b shifts are taken repeatedly in sequential order, hence needing at least b b points to obtain the optimal order of L 2 discrepancy....