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In this paper, we are concerned with the problem of designing optimal linear hashing files for orthogonal range retrieval. Through the study of performance expressions, we show that optimal basic linear hashing files and optimal recursive linear hashing files for orthogonal range retrieval can be produced, in certain cases, by a greedy method called the MMI (minimum marginal increase) method; and it is pointed out that optimal linear hashing files for partial match retrieval need not be optimal for orthogonal range retrieval.