  According to Aistleitner and Weimar, there exist two-dimensional (double)
infinite matrices whose star-discrepancy $D_N^{*s}$ of the first $N$ rows and
$s$ columns, interpreted as $N$ points in $[0,1]^s$, satisfies an inequality of
the form $$D_N^{*s} \leq \sqrt{\alpha}
\sqrt{A+B\frac{\ln(\log_2(N))}{s}}\sqrt{\frac{s}{N}}$$ with $\alpha =
\zeta^{-1}(2) \approx 1.73, A=1165$ and $B=178$. These matrices are obtained by
using i.i.d sequences, and the parameters $s$ and $N$ refer to the dimension
and the sample size respectively. In this paper, we improve their result in two
directions: First, we change the character of the equation so that the constant
$A$ gets replaced by a value $A_s$ dependent on the dimension $s$ such that for
$s>1$ we have $A_s<A$. Second, we generalize the result to the case of the
(extreme) discrepancy. The paper is complemented by a section where we show
numerical results for the dependence of the parameter $A_s$ on $s$.
