  The declustering problem is to allocate given data on parallel working
storage devices in such a manner that typical requests find their data evenly
distributed on the devices. Using deep results from discrepancy theory, we
improve previous work of several authors concerning range queries to
higher-dimensional data. We give a declustering scheme with an additive error
of $O_d(\log^{d-1} M)$ independent of the data size, where $d$ is the
dimension, $M$ the number of storage devices and $d-1$ does not exceed the
smallest prime power in the canonical decomposition of $M$ into prime powers.
In particular, our schemes work for arbitrary $M$ in dimensions two and three.
For general $d$, they work for all $M\geq d-1$ that are powers of two.
Concerning lower bounds, we show that a recent proof of a
$\Omega_d(\log^{\frac{d-1}{2}} M)$ bound contains an error. We close the gap in
the proof and thus establish the bound.
