Hammersley Point Sets and Inverse of Star-Discrepancy

We establish the existence of $N$-point sets in dimension $d$ whose star-discrepancy is bounded above by $2.4631832\sqrt{\frac{d}{N}}$, where the numerical constant improves upon all previously known bounds. This improvement is obtained by combining a recent result by Gnewuch on bracketing numbers in high dimensions with discrepancy bounds for Hammersley point sets due to Atanassov in dimensions $1\le d\le 4$.