Optimality and uniqueness of the Leech lattice among lattices
Abstract
We prove that the Leech lattice is the unique densest lattice in R24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R24 can exceed the Leech lattice's density by a factor of more than 1+1.65*10(-30), and we give a new proof that E8 is the unique densest lattice in R8.
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