Bounds on the maximum number of clear two-factor interactions for 2m-p designs of resolution III and IV

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.