A BOUND, AND A CONJECTURE, ON THE MAXIMUM LATTICE-PACKING DENSITY OF A SUPERBALL

We obtain explicit lower bounds on the lattice packing densities delta (L) of superballs G of quite a general nature, and we conjecture that as the dimension n approaches infinity, the bounds are asymptotically exact. If the conjecture were true, it would follow that the maximum l attice-packing density of the l(sigma)-ball \x1\sigma +...+ \x(n)\sigm a less-than-or-equal-to 1 is 2-n(1+o(1)) for each sigma in the interva l 1 less-than-or-equal-to sigma less-than-or-equal-to 2.