Bound on the maximum number of clear two-factor interactions for 2n-(n-k) designs

Clear effects criterion is an important criterion for selecting fractional factorial designs [1]. Tang et al. [2] derived upper and lower bounds on the maximum number of clear two-factor interactions (2fi's) in 2n-(n-k) designs of resolution III and IV by constructing 2n-(n-k) designs. But the method in [2] does not perform well sometimes when the resolution is III. This article modifies the construction method for 2n-(n-k) designs of resolution III in [2]. The modified method is a great improvement on that used in [2].