This talk gives an introduction into admissible lattices. We first take a look at some basic geometric properties of such lattices and how they are constructed. After that, we show that the L^\infty discrepancy of admissible lattices with respect to axis-parallel rectangles is logarithmically small, if compared to the measure of the rectangle.
Reference: M. M. Skriganov, Constructions of uniform distributions in terms of geometry of numbers. Algebra i Analiz, 1994, Volume 6, Issue 3, Pages 200–230