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This paper presents the algorithm "DETMAX" whose purpose is to construct experimental designs that are "D-optimal," These are designs for which the determinant of X'X is maximum, where X is the "matrix of independent variables" in the usual linear model y = Xβ + ε. Although the algorithm does not guarantee D-optimality, it has performed well in many cases where D-optimal designs are known. Five examples are given, illustrating the use of DETMAX to construct designs "from scratch" and to augment existing data. A FORTRAN listing is available on request. [ABSTRACT FROM AUTHOR]