Réseaux entiers unimodulaires sans racines en dimension 27 et 28
- R. Bacher, B. B. Venkov
- Preprint No. 332, Inst. Fourier, Grenoble
The highest possible minimal norm of a unimodular lattice is determined in dimensions n ≤ 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8.1020 in dimension 33). Unimodular lattices with no roots exist if and only if n ≥ 23, n 6= 25.