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We consider the problem of constructing multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We model this as a combinatorial optimization problem of number arrangements in a matrix. This approach gives a general technique for deriving lower bounds on the distortion at given channel rates. This technique is constructive, thus allowing an algorithm that gives an upper bound. For the case of two communication channels with equal rates, the bounds coincide, thus giving the precise lowest achievable distortion at fixed rates. The bounds are within a small constant for a higher number of channels. To the best of our knowledge, this is the first result involving systems with more than two communication channels.