Article
Discrepancy of Linearly Digit 2 Scrambled Zaremba Point Sets
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Abstract
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 π l(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.
Keywords
L 2 discrepancy, generalized Hammersley point set, linear digit scrambling.
Citation
Faure, H. & Pirsic, F. P. A. G. (2011). Discrepancy of linearly digit 2 scrambled zaremba point sets. Uniform Distribution Theory, 6(2), 59–81.
H. Faure and F. P. A. G. Pirsic, “Discrepancy of linearly digit 2 scrambled zaremba point sets,” Uniform Distribution Theory, vol. 6, no. 2, pp. 59–81, 2011.
Faure H, Pirsic FPAG. Discrepancy of linearly digit 2 scrambled zaremba point sets. Uniform Distribution Theory. 2011;6(2):59–81.
Faure, H. and Pirsic, F. P. A. G. (2011), ‘Discrepancy of linearly digit 2 scrambled zaremba point sets’, Uniform Distribution Theory, 6(2), pp. 59–81.
Faure, Henri, and Friedrich Pillichshammer and Gottlieb Pirsic. “Discrepancy of Linearly Digit 2 Scrambled Zaremba Point Sets.” Uniform Distribution Theory, vol. 6, no. 2, 2011, pp. 59–81.
Faure, Henri, and Friedrich Pillichshammer and Gottlieb Pirsic. “Discrepancy of Linearly Digit 2 Scrambled Zaremba Point Sets.” Uniform Distribution Theory 6, no. 2 (2011): 59–81.
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Published by: Engineering Journals
