  For a point set of $n$ elements in the $d$-dimensional unit cube and a class
of test sets we are interested in the largest volume of a test set which does
not contain any point. For all natural numbers $n$, $d$ and under the
assumption of a $delta$-cover with cardinality $\vert \Gamma_\delta \vert$ we
prove that there is a point set, such that the largest volume of such a test
set without any point is bounded by $\frac{\log \vert \Gamma_\delta \vert}{n} +
\delta$. For axis-parallel boxes on the unit cube this leads to a volume of at
most $\frac{4d}{n}\log(\frac{9n}{d})$ and on the torus to $\frac{4d}{n}\log
(2n)$.
