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In this paper balanced optimal fractional factorial designs of 2m series which allow the estimation of the general mean, main effects and two factor interactions are described. Such designs are presented for each m with 4 < m < 6, and for a range of practical values of N, where N denotes the total number of level-combinations.The covariance matrices of the estimates of the effects are also presented for each design, with a set of simple formulae for calculating these estimates.

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