A probability estimate for the discrepancy of Korobov lattice points

Bykovskii (2002) obtained the best current upper estimate for the minimum discrepancy of the Korobov lattice points from the uniform distribution. We show that this estimate holds for almost all $s$-dimensional Korobov lattices of $N$ nodes, where $s\geqslant 3$, and $N$ is a prime number.
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