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Article Dans Une Revue Uniform Distribution Theory Année : 2011

L_2 discrepancy of linearly digit scrambled Zaremba point sets

Henri Faure
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Friedrich Pillichshammer
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Gottlieb Pirsic
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Résumé

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. For the construction of such point sets one needs sequences of permutations of the form πl(k) = αk + l (mod b) for k, l ∈ {0, . . . , b − 1}. As a corollary we obtain a condition on these sequences which yields the best possible order of L_2 discrepancy of generalized Zaremba point sets in the sense of Roth’s lower bound, with very small leading constants.
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Dates et versions

hal-01273539 , version 1 (12-02-2016)

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  • HAL Id : hal-01273539 , version 1

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Henri Faure, Friedrich Pillichshammer, Gottlieb Pirsic. L_2 discrepancy of linearly digit scrambled Zaremba point sets. Uniform Distribution Theory, 2011, 6 (2), pp.59-81. ⟨hal-01273539⟩
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