Local optimality of the E_8 lattice for the packing-covering problem

Let $\mathsf{E}_8$ denote the root lattice in dimension $8$. A lattice is a locally optimal solution to the lattice packing-covering problem if no sufficiently small deformation improves the relevant packing-covering objective. The E_8 local-optimality conjecture. The root lattice $\mathsf{E}_8$ gives a locally optimal solution for the lattice packing-covering problem. The source says that computational experiments support this claim, while noting that the required converse condition is unavailable because the relevant feasible set need not be separatable.