Dual vectors and lower bounds for the nearest lattice point problem

We prove that given a point ~z outside a given lattice L then there is a dual vector which gives a fairly good estimate for how far from the lattice the vector is. To be more precise, there is a set of translated hyperplanes Hi such that L S iHi and d(~z; S iHi) 1 6n+1 d(~z; L). Warning: Essentially this paper has been published in Combinatorica and is hence subject to copyright restrictions. It is for personal use only.