********************************************************************** * The data in this directory are * Copyright (C) 2008 Nils-Peter Skoruppa * * Distributed under the terms of the GNU General Public License (GPL) * http://www.gnu.org/licenses/ ********************************************************************** This directory contains the 55475 even unimodular lattices of rank 72 and the 55475 even lattices of rank 70 and determinant 71 which possess an automorphism of order 71 whose fixed lattice has no vector of square length shorter than $8$. See the *.info files for details. The file ext72.pdf gives some hints for the generation of these lattices, which was done on the Cluster (socalled 'Rubens Cluster') of the University of Siegen. --- Added February 2013: Meanwhile we could show that all these lattices have a vector with square length strictly less than $8$. Therefrore, no extremal lattice of rank 72 possesses an automorphism of order $71$.