Improving a constant in high-dimensional discrepancy estimates

Hendrik Pasing, Christian Weiss

For all $s\geq1$ and $N\geq1$ there exist sequences $(z_1,\dots,z_N)$ in $[0,1]^s$ such that the star-discrepancy of these points can be bounded by \[ D_N^*(z_1,\dots,z_N)eq c\frac{qrt{s}}{qrt{N}}. \] In practice it is desireable to obtain low values of $c$. The best known value for the constant is $c=10$ as has been calculated by Aistleitner. In this paper we improve the bound to $c=9$.