Perfect, Strongly Eutactic Lattices Are Periodic Extreme
نویسنده
چکیده
We introduce a parameter space for periodic point sets, given as a union of m translates of a point lattice. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality. Using these criteria we prove that perfect, strongly eutactic lattices cannot be locally improved to yield a denser periodic sphere packing. This in particular implies that the densest known lattice sphere packings in dimension d ≤ 8 and d = 24 cannot locally be modified to yield a periodic sphere packing with greater density.
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