Construction of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 2^{m - (m - k)}_{{\rm{III}}} $$\end{document} Designs with the Maximum Number of Clear Two-factor Interactions

It is useful to know the maximum number of clear two-factor interactions in a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 2^{m - (m - k)}_{{\rm{III}}} $$\end{document} design. This paper provides a method to construct a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ 2^{m - (m - k)}_{{\rm{III}}} $$\end{document} design with the maximum number of clear two-factor interactions. And it is proved that the resulting designs have more clear two-factor interactions than those constructed by Tang et al. [6]. Moreover, the designs constructed are shown to have concise grid representations.