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Published online by Cambridge University Press: 26 February 2010
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.