We study worst-case signal compression under an $\ell^2$ energy constraint, with coordinate-dependent quantization precisions. The compression problem is reduced to counting lattice points in a diagonal ellipsoid. Under balanced precision profiles, we obtain explicit, dimension-dependent upper bounds on the logarithmic codebook size. The analysis refines Landau's classical lattice point estimates using uniform Bessel bounds due to Olenko and explicit Abel summation.

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