Leech-lattice conjecture for quantum paving in dimension 24

Let $\Lambda$ be a Leech lattice in phase space of dimension $24$, with arbitrary fixed density greater than $1$. The Leech-lattice conjecture. There exists a Leech lattice that solves the quantum paving problem. The claim is motivated by the Leech lattice's optimality for sphere packing, universal optimality for energy minimization, and strong known covering properties, but it remains open; the relevant lattice may require a suitable permutation of the base vectors or rotation, rather than being the standard realization.