For a rational quadratic disk-slab on a shifted integer grid with the Babai point outside the constructed inner ellipse, exactly four integer levels of the reduction-selected functional can be occupied.
On Lov´ asz’ lattice reduction and the nearest lattice point problem.Combina- torica, 6(1):1–13, 1986
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A Sharp Four-Layer Theorem for Integer-Occupied Slices of a Planar Disk-Slab
For a rational quadratic disk-slab on a shifted integer grid with the Babai point outside the constructed inner ellipse, exactly four integer levels of the reduction-selected functional can be occupied.