Journal of Complexity ( IF 1.338 ) Pub Date : 2019-10-18 , DOI: 10.1016/j.jco.2019.101441
Friedrich Pillichshammer; Mathias Sonnleitner

We show that the isotropic discrepancy of a lattice point set can be bounded from below and from above in terms of the spectral test of the corresponding integration lattice. From this result we deduce that the isotropic discrepancy of any $N$-element lattice point set in [0,1)${}^{d}$ is at least of order ${N}^{-1∕d}$. This order of magnitude is best possible for lattice point sets in dimension $d$.

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