Recent Progress in Improvement of Extreme Discrepancy and Star Discrepancy of One-dimensional Sequences

Victor Ostromoukhov (1)

1 R3AM - Rendu Réaliste pour la Réalité Augmentée Mobile

In this communication, we report on recent progress in improvement of extreme discrepancy and star discrepancy of one-dimensional sequences. Namely, we present a permutation of "Babylonian" sequences in base 60, which improves the best known results for star discrepancy obtained by Henri Faure in 1981, and a permutation of sequences in base 84, which improves the best known results for extreme discrepancy obtained by Henri Faure in 1992. Our best result for star discrepancy in base 60 is 32209/(35400 log 60) \approx 0.222223 (Faure's best result in base 12 is 1919/(3454 log 12) \approx 0.223585); our best result for extreme discrepancy in base 84 is 130/(83 \log 84) \approx 0.353494 (Faure's best result in base 36 is 23/(35 log 6) \approx 0.366758).

Domaines: Informatique [cs]

Victor Ostromoukhov. Recent Progress in Improvement of Extreme Discrepancy and Star Discrepancy of One-dimensional Sequences. Pierre L'Ecuyer, Art B. Owen. Monte-Carlo and Quasi-Monte Carlo Methods 2008, Springer-Verlag, pp.561-572, 2009, ⟨10.1007/978-3-642-04107-5_36⟩. ⟨hal-01437781⟩