Stacking Spheres

Sounds like the mathematical correlative of herding cats.

wikipedia wrote:

In 2016, Maryna Viazovska announced a proof that the E8 lattice provides the optimal packing (regardless of regularity) in eight-dimensional space,[10] and soon afterwards she and a group of collaborators announced a similar proof that the Leech lattice is optimal in 24 dimensions.[11] This result built on and improved previous methods which showed that these two lattices are very close to optimal.[12] The new proofs involve using the Laplace transform of a carefully-chosen modular function to construct a radially-symmetric function f such that f and its Fourier transform f̂ both equal one at the origin, and both vanish at all other points of the optimal lattice, with f negative outside the central sphere of the packing and f̂ positive. Then, the Poisson summation formula for f is used to compare the density of the optimal lattice with that of any other packing.[13] Before the proof had been formally refereed and published, mathematician Peter Sarnak called the proof "stunningly simple" and wrote that "You just start reading the paper and you know this is correct."

Maybe.

What I found interesting is that an optimal sphere-packing scheme uses up 74% of the space. A random, uncontrolled scheme uses up on average just 64%.

I wouldn't have guessed a ten percent improvement.