he's referring to maximal compression in 8 dimensions, proved here (h/t @1623) https://arxiv.org/abs/1603.04246
arXiv.org The sphere packing problem in dimension 8 In this paper we prove that no packing of unit balls in Euclidean space $\mathbb{R}^8$ has density greater than that of the $E_8$-lattice packing.