2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98222We show that the integers in the HMM LLL HNF algorithm have bit length O(m.log(m.B)), where m is the number of rows and B is the maximum square length of a row of the input matrix. This is only a little worse than the estimate O(m.log(B)) in the LLL algorithm.10 pagesNumber Theory11Y16text