A note on the construction of blocked two-level designs with general minimum lower order confounding

• This paper gives the construction method of B-GMC 2n−m:2r2n−m:2r designs with 5N/16+1≤n≤N/25N/16+1≤n≤N/2, where N=2n−mN=2n−m.
• We show that each B-GMC blocked design has a common specific structure.
• Examples are included to illustrate the developed theory.

Blocked designs are useful in experiments. The general minimum lower order confounding (GMC) is an elaborate criterion which was proposed for selecting optimal fractional factorial designs. Zhang and Mukerjee (2009b) extended the GMC criterion to the B-GMC criterion for selecting a 2n−m:2r2n−m:2r design, where 2n−m:2r2n−m:2r denotes a two-level regular blocked design with N=2n−mN=2n−m runs, nn treatment factors and 2r2r blocks. This paper gives the first construction method of B-GMC 2n−m:2r2n−m:2r designs with 5N/16+1≤n≤N/25N/16+1≤n≤N/2. The results indicate that under isomorphism, with suitable choice of the blocking factors, each B-GMC blocked design has a common specific structure. Examples are included to illustrate the developed theory.