There exist lattices in dimensions having hypersphere
packing densities satisfying
is the Riemann zeta function. However, the
proof of this theorem is nonconstructive and it is still not known how to actually
construct packings that are this dense.
See alsoHermite Constants
Explore with Wolfram|Alpha
ReferencesConway, J. H. and Sloane, N. J. A. Sphere
Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, pp. 14-16,
1993.Pach, J. and Agarwal, P. K. Combinatorial
Geometry. New York: Wiley, 1995.
Referenced on Wolfram|AlphaMinkowski-Hlawka Theorem
Cite this as:
Weisstein, Eric W. "Minkowski-Hlawka Theorem."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Minkowski-HlawkaTheorem.html