Article
An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval
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Abstract
It is known that there is a constant c > 0 such that for every sequence x 1 , x 2 , . . . in [0, 1) we have for the star discrepancy D N ∗ of the first N elements of the sequence that ND∗ ≥ c·log N holds for infinitely many N. Let c∗ N be the supremum of all such c with this property. We show c∗ > 0.065664679 . . . , thereby slightly improving the estimates known until now.
Keywords
uniform distribution, discrepancy.
Citation
Larcher, G. & Puchhammer, F. (2016). An improved bound for the star discrepancy of sequences in the unit interval. Uniform Distribution Theory, 11(1), 1–14. https://doi.org/10.1515/udt-2016-0001
G. Larcher and F. Puchhammer, “An improved bound for the star discrepancy of sequences in the unit interval,” Uniform Distribution Theory, vol. 11, no. 1, pp. 1–14, 2016, doi: 10.1515/udt-2016-0001.
Larcher G, Puchhammer F. An improved bound for the star discrepancy of sequences in the unit interval. Uniform Distribution Theory. 2016;11(1):1–14. doi:10.1515/udt-2016-0001.
Larcher, G. and Puchhammer, F. (2016), ‘An improved bound for the star discrepancy of sequences in the unit interval’, Uniform Distribution Theory, 11(1), pp. 1–14. Available at: https://doi.org/10.1515/udt-2016-0001.
Larcher, Gerhard, and Florian Puchhammer. “An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval.” Uniform Distribution Theory, vol. 11, no. 1, 2016, pp. 1–14. https://doi.org/10.1515/udt-2016-0001.
Larcher, Gerhard, and Florian Puchhammer. “An Improved Bound for the Star Discrepancy of Sequences in the Unit Interval.” Uniform Distribution Theory 11, no. 1 (2016): 1–14. https://doi.org/10.1515/udt-2016-0001.
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Published by: Engineering Journals
