arXiv:2610.33085v1 Announce Type: new Abstract: We prove that the unnormalized discrepancy function of every $n$-point set in the unit square has absolute value at least $c\sqrt{1+\log n}$ on a set of measure at least $\eta$, with absolute constants $c,\eta>0$. Consequently, its $L_p$-quasinorm is bounded below by $c\,\eta^{1/p} \sqrt{1+\log n}$ for every $p>0$.
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