An ellipsoid packing in E 3 of unexpected high density

A. Bezdek and W. Kuperberg constructed a nonlattice packing of congruent ellipsoids in Euclidean 3-space E3 with density 0·7459 …, which exceeds the density σL2 = 0·74048… of the densest lattice packing of spheres and hence of ellipsoids in E3. G. Kuperberg improved this to 0·7533… We improve this slightly to 0·7549…. In our case the quotient of the largest and the smallest halfaxis of the ellipsoids is <42, so the ellipsoids are not too degenerate. If one combines G. Kuperberg's refinement and ours, one obtains a packing density of 0·7585…