The great open discrepancy conjecture in dimension at least three

Let $D(m,d)_\infty$ denote the minimal $L_\infty$ discrepancy of an $m$-point set in dimension $d$, and let $C(d)>0$ depend only on $d$. Discrepancy lower-bound conjecture. For $d\ge 3$,

$$D(m,d)_\infty \ge C(d)m^{-1}(\log m)^{d-1}.$$

This is the conjectured optimal-order lower bound for the star discrepancy in dimensions at least three and is described in the source as an excruciatingly difficult open problem.