The star-discrepancy lower-bound conjecture

Let $m$ points be chosen in $[0,1)^d$, and let $D(m,d)_\infty$ denote the infimum of their $L_\infty$ discrepancy. Star-discrepancy lower-bound conjecture. For $d\ge 3$,

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

This is the classical great open problem in discrepancy theory, formulated as an excruciatingly difficult problem; the optimal logarithmic exponent is known in several weaker settings but remains open for the $L_\infty$ discrepancy in dimensions at least three.