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Constructive packings of cross polytopes
Published online by Cambridge University Press: 26 February 2010
Abstract
The n-dimensional cross polytope, |x|+|x2|+…+|xn≤1, can be lattice packed with density δ satisfying
but proofs of this, such as the Minkowski-Hlawka theorem, do not actually provide such packings. That is, they are nonconstructive. Here we exhibit lattice packings whose density satisfies only
but by a highly constructive method. These are the densest constructive lattice packings of cross polytopes obtained so far.
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- Research Article
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- Copyright © University College London 1991
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