The covolume conjecture for 48-dimensional lattices of minimal norm 6

Let $L\subset\mathbb{R}^{48}$ be a lattice with minimal norm $\sqrt{6}$. Covolume conjecture. If there is $x\in L$ with $\sqrt{8}<|x|<\sqrt{10}$, then $L$ has covolume greater than $1$. The paper describes this as a bold conjecture and a research direction, with no numerical evidence supplied; it is intended to support the optimality of the relevant extremal lattice packing.