As accessible on the "past" link above, there was a good discussion earlier on this solution of sphere-packing in d = 8 and d = 24, featuring an epic explanatory comment: https://news.ycombinator.com/item?id=11394534
Note this is from 2016.
http://oeis.org/A257479 Maximal kissing number in n dimensions: maximal number of unit spheres that can touch another unit sphere.