Density doubling, double-circulants, and new sphere packings

Vardy, Alexander

doi:10.1090/S0002-9947-99-02169-8

Density doubling, double-circulants, and new sphere packings
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Trans. Amer. Math. Soc. 351 (1999), 271-283 Request permission

Abstract:

New nonlattice sphere packings in dimensions 20, 22, and 44–47 that are denser than the best previously known sphere packings were recently discovered. We extend these results, showing that the density of many sphere packings in dimensions just below a power of 2 can be doubled using orthogonal binary codes. This produces new dense sphere packings in $\mathbb R^n$ for $n = 25,26,\dots ,31$ and $55,56,\dots ,63$. For $n = 27,28,29,30$ the resulting packings are denser than any packing previously known.

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