On the minimum volume of a perturbed unit cube

Abstract

We give exact bounds to the minimum volume of a parallelepiped whose spanning vectors are perturbations of the n unit vectors by vectors of length at most e. This extends Micciancio's recent sharp bounds to all possible values of e. We also completely determine all possible perturbations with length at most e that achieve this minimum volume. © Springer-Verlag Berlin Heidelberg 2002.