A new series of main effects plus one plan for 2m factorial experiments with m=4λ±1 and 2m runs

An MEP.1 plan for a 2m factorial experiment is able to search and estimate one possible nonzero interaction effect along with estimating the general mean and main effects. Construction of such a plan has been tackled by several authors. Some of these works are developed for all m, in which are focused on m=2h−1 or m=4λ−1 for positive integers h>2 and λ≥2. This leads to a gap for having MEP.1 plans with well-structured runs set and probably with a reasonable number of treatments for m≠2h−1 or 4λ−1. In this paper, we characterize and present a series of highly structured MEP.1 plans for all odd m=4λ±1,λ≥2, with N=2m runs. From these designs one can obtain the MEP.1 plans for even m with N=2m+1 treatments. The exemptions are m= 8 and 9 for which we have 1 or 2 extra runs.