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This guarantee is true for any number of dimensions. Subsequent to this work, Bhatia et al. [4] have proved that such a performance bound is essentially optimal for this kind of scheme, and have also extended our results to the case where the number of disks is a product of the form &kgr;1 * &kgr;2 * … * &kgr;t where the &kgr;ts need not all be 2.