A note on the dispersion of admissible lattices

10/24/2017

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by   Mario Ullrich, et al.

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In this note we show that the volume of axis-parallel boxes in R^d which do not intersect an admissible lattice L⊂R^d is uniformly bounded. In particular, this implies that the dispersion of the dilated lattices N^-1/dL restricted to the unit cube is of the (optimal) order N^-1 as N goes to infinity. This result was obtained independently by V.N. Temlyakov (arXiv:1709.08158).