“John Leech, in the 1960s, used one of Golay's codes to build an incredibly dense packing of twenty-four dimensional spheres, in a configuration now known as the Leech lattice. It's a crowded place, the Leech lattice, where each of the twenty-four-dimensional spheres touches 196,560 of its neighbors. We still don't know whether it's the tightest possible twenty-four-dimensional packing, but in 2003, Henry Cohn and Abhinav Kumar proved that if a denser lattice exists, it beats Leech by a factor of at most

1.00000000000000000000000000000165.

In other words: close enough”