Barnes–Wall lattice
In mathematics, the Barnes–Wall lattice Λ16, discovered by Eric Stephen Barnes and G. E. Wall, is the 16-dimensional positive-definite even integral lattice of discriminant 28 with no norm-2 vectors. It is the sublattice of the Leech lattice fixed by a certain automorphism of order 2, and is analogous to the Coxeter-Todd lattice.
The automorphism group of the Barnes-Wall lattice has order 89181388800 = 221 35 52 7 and has structure 21+8 PSO8+.
The genus of the Barnes-Wall lattice was described by and contains 24 lattices; all the elements other than the Barnes-Wall lattice have root system of maximal rank 16.
The Barnes-Wall lattice is described in detail in.
