On construction of general minimum lower order confounding 2n−m designs with N/4+1≤n≤9N/32N/4+1≤n≤9N/32

The construction of optimal 2n−m designs with N/4+1≤n≤9N/32N/4+1≤n≤9N/32, where N=2n−m is the run size, and their comparison under different criteria have received significant attention in recent years. In this paper, we first prove that the MaxC2 design with n=N/4+1 is unique up to isomorphism and has general minimum lower order confounding (GMC). Then, by utilizing the theory of doubling and second order saturated resolution IV designs extended by Zhang and Cheng (2010), we propose a method of constructing GMC design and obtain all the GMC designs with N/4+1≤n≤9N/32N/4+1≤n≤9N/32 up to isomorphism. Finally, we show that, for all N and n in the above range, the MA and GMC designs are different.