Extremal self‐dual lattices exist only in dimensions 1 to 8, 12, 14, 15, 23, and 24
John H. Conway, Andrew M. Odlyzko, Neil J.A. Sloane · Mathematika · 1978
It is known that if Λ is a self-dual lattice in ℝn, then If equality holds the lattice is called extremal. In this paper we find all the extremal lattices: there are unique lattices in dimensions 1, 2, 3, 4, 5, 6, 7, 8, 12, 14, 15, 23, 24 and no others.