The grand discrepancy conjecture for infinite sequences

Let $s\in\mathbb{N}$ and let $\mathcal{S}$ be a sequence in $[0,1)^s$. Write $D_N^{\ast}(\mathcal{S})$ for its star discrepancy at $N$ points. Grand discrepancy conjecture. For every $s\in\mathbb{N}$ there exists a constant $c_s>0$ such that, for every sequence $\mathcal{S}$ in $[0,1)^s$,

$$D_N^{\ast}(\mathcal{S})\geq c_s\frac{(\log N)^s}{N}$$

for infinitely many $N$. Except in dimension one, this would close the gap between the known lower and upper bounds for the star discrepancy of infinite sequences; the conjecture is presented as a major open problem in discrepancy theory, although the source notes that it is not universally accepted.