Table of Strongly Perfect Lattices

 Keywords: tables, perfect lattices, quadratic forms

 Part of the Catalogue of Lattices which is a joint project of Gabriele Nebe, RWTH Aachen university ( and Neil J. A. Sloane, (

Last modified Mai 2019

All known Strongly Perfect Lattices up to dimension 26

This table of strongly perfect lattices is complete through 13 dimensions, in dimension 14,15,16 it is complete assuming that also the dual lattice is strongly perfect.


The table is based on the one in the paper by Boris Venkov, Reseaux and designs spheriques. There are two additional entries in dimension 16, discovered by Sihuang Hu and Gabriele Nebe. By a result by Christine Bachoc and Boris Venkov

all extremal even unimodular lattices in dimensions congruent to 0 or 8 mod 24 are strongly perfect,

all extremal even 2-modular lattices in dimensions congruent to 0 or 4 mod 16 are strongly perfect and

all extremal even 3-modular lattices in dimensions congruent to 0 or 2 mod 12 are strongly perfect.