Improving a constant in high-dimensional discrepancy estimates | Zendy

Hendrik Pasing | Zendy; Christian Weiß | Zendy

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Improving a constant in high-dimensional discrepancy estimates

Author(s) -

Hendrik Pasing,

Christian Weiß

Publication year - 2020

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim2021067p

Subject(s) - constant (computer programming) , bounded function , value (mathematics) , mathematics , star (game theory) , upper and lower bounds , combinatorics , physics , mathematical analysis , statistics , computer science , programming language

For all $s \geq 1$ and $N \geq 1$ there exist sequences $(z_1,\ldots,z_N)$ in $[0,1]^s$ such that the star-discrepancy of these points can be bounded by $$D_N^*(z_1,\ldots,z_N) \leq c \frac{\sqrt{s}}{\sqrt{N}}.$$ The best known value for the constant is $c=10$ as has been calculated by Aistleitner in \cite{Ais11}. In this paper we improve the bound to $c=9$.

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