A Note on Optimal Unimodular Lattices Original Research Article

The highest possible minimal norm of a unimodular lattice is determined in dimensionsnless-than-or-equals, slant33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8.1020in dimension 33). Unimodular lattices with no roots exist if and only ifngreater-or-equal, slanted23,n≠25.