Bounds on the maximum number of clear two‐factor interactions for 2^<i>m‐p</i> designs of resolution III and IV

Abstract The authors derive upper and lower bounds on the maximum number of clear two‐factor interactions in 2 m−p fractional factorial designs of resolution III and IV. A two‐factor interaction is said to be clear if it is not aliased with any main effect or with any other two‐factor interaction. The lower bounds are obtained by exhibiting specific designs. By comparing the bounds with the values of the maximum number of clear two‐factor interactions in cases where it is known, one concludes that the construction methods perform quite well.