  For $\varepsilon\in(0,1/2)$ and a natural number $d\ge 2$, let $N$ be a
natural number with \[ N \,\ge\, 2^9\,\log_2(d)\,
\left(\frac{\log_2(1/\varepsilon)}{\varepsilon}\right)^2. \] We prove that
there is a set of $N$ points in the unit cube $[0,1]^d$, which intersects all
axis-parallel boxes with volume $\varepsilon$. That is, the dispersion of this
point set is bounded from above by $\varepsilon$.
