Tusnády's problem, the transference principle, and non-uniform QMC sampling

Christoph Aistleitner, Dmitriy Bilyk, Aleksandar Nikolov

It is well-known that for every $N\ge 1$ and $d\ge 1$ there exist point sets $x_1,\dots ,x_N\in [0,1{]}^d$ whose discrepancy with respect to the Lebesgue measure is of order at…