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The problem of implementing multidimensional quantizers is discussed. A general equation is derived that can be used to evaluate the performance of multidimensional compandors. It is demonstrated that the optimal compandor must be conformal almost everywhere. An example is given to show that asymptotically optimal performance could be obtained through nonconformal companding schemes. Random quantizers are discussed and two techniques are evaluated for reducing memory and computation time in the implementation of such devices.