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Fractional designs involve selection from a given set of experimental treatments as subset of treatments to make-up a specified design measure that has such statistical properties as balance, high relative efficiency, D-optimality etc. For decades statisticians have relied on the use Defining Contracts (DC), and Latin Squares (LS) to construct fractional factorial designs. But these methods are shown to have very limited range of applications and sometimes produce designs that are singular. This paper introduces the method of Concentric Balls (CB) for constructing non-singular fractional designs. Each ball consists of treatments that are of equal distance from the center and using a set of rules for selecting treatments from a ball the CB method yields a small set of admissible designs. The best member of this admissible set is the desired design:{Best in the sense of maximizing the determinant of the normalized information matrix or maximizing the relative efficiency of the factorial effects.}Numerical examples show that the CB method covers every range of experimental design conditions and can produce fractional designs that are D-optimal.

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