A lower bound for the number of singular staturated main effect plans of anS m factorial

Summary A fraction consisting ofm(s−1)+1 observations taken atm(s−1)+1 treatment combinations of ans ^m factorial with the aim to estimate the mean and them(s−1), main effect single degree of freedom parameters is called a saturated main effect plan. If the design matrix of such a fraction is singular, then the fraction is called a singular saturated main effect plan. This paper presents a lower bound on the number of singular saturated main effect plans. Research supported by N.R.C. Grant No. A07204.