  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 $c=9$.
