Abstract
Summary Fractional factorial designs of resolution IV permit estimation of all the main effects with no aliasing by two-factor interactions. This paper produces a lower bound for the number of observations required for a general fractional factorial design to be of resolution IV. This lower bound agrees with a lower bound obtained by Rao for orthogonal arrays of strength 3. In addition, it is proved that this lower bound is attainable for the t. 2n factorial design series for t even and n ≡ 3 (mod 4) in plans which permit orthogonal estimation of the main effects. Finally, Webb's conjecture that there exist no resolution IV 2n factorial designs with 2n runs except for those constructed by the fold-over technique is proved to be valid.
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