Bases of minimal vectors in lattices, III

Jacques Martinet, Achill Schürmann

Published 2011-05-30, updated 2011-09-02Version 2

We prove that all Euclidean lattices of dimension $n\le 9$ which are generated by their minimal vectors, also possess a basis of minimal vectors. By providing a new counterexample, we show that this is not the case for all dimensions $n\ge 10$.