New sphere-packing record stems from an unexpected source
The advantage of Rogers’ method was that you didn’t have to start with a particularly efficient lattice to get an efficient sphere packing. You just had to choose the right ellipsoid. But this introduced a new complication. Unlike a sphere, which is completely defined by a single number — its radius — an ellipsoid is defined by several axes of different lengths. The higher the dimension, the greater the number of directions you can stretch your ellipsoid in, and the more options you have for wha