A note on the existence of sequences with small star discrepancy (Q2465294)

By a well-known result of \textit{S. Heinrich} et al. [Acta Arith. 96, 279--302 (2001; Zbl 0972.11065)] there exists a set \(P\) of \(n\) points in \([0,1]^{s}\) such that the star-discrepancy \(D^{*}_{n,s}\) is \(\leq C \cdot \sqrt{\frac{s}{n}}\) (for some constant \(C\)). In the present paper this result is extended to infinite sequences \(P\) and a similar upper bound for \(D^{*}_{n,s} (P)\) (with an additional logarithmic factor) is obtained.