An upper bound on the minimal dispersion

For ε∈(0,1∕2) and a natural number d≥2, let N be a natural number with N≥29log2(d)log2(1∕ε)ε2.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 ε. That is, the dispersion of this point set is bounded from above by ε.