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/d L 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).Such lattices play a crucial role in the geometry of numbers, see e.g. [3,8] and the references therein, especially in the theory of Diophantine approximation. Moreover, they are among the most important explicit constructions of point sets, which satisfy various uniform distribution properties, like the optimal order of the discrepancy [7,17]. They attracted quite a lot of attention in numerical analysis as the corresponding point sets seem to serve as an optimal and universal choice as nodes for corresponding cubature rules, see e.g. [6,10,12,17,20,21,27,28,29]. See also [14,16,21] for surveys on the state of the art in numerical integration. Apart from the concepts and geometric quantities that are important for the above, there is an increasing interest in the dispersion of a point set. For d ∈ N and a point set P ⊂ [0, 1] d , the dispersion of P is defined bywhere the supremum is over all axis-parallel boxes B = I 1 × · · · × I d with intervals I ℓ ⊂ [0, 1], and |B| denotes the volume of B. This quantity was proven to be essential for various numerical problems including optimization [13], approximation of high-dimensional rank-1 tensors [2,15] and, very recently, in the study of Marcinkiewicz-type discretization theorems [22,23,24]. Moreover, algorithms for finding such a box with maximal volume, with a motivation coming from information theory, are also of some interest, see [4,5,11] and references therein. In all these contexts, it is desirable to have tight bounds Date: September 3, 2018.