Construction of blocked two-level regular designs with general minimum lower order confounding

Zhang et al. (2008) proposed a general minimum lower order confounding (GMC for short) criterion, which aims to select optimal factorial designs in a more elaborate and explicit manner. By extending the GMC criterion to the case of blocked designs, Wei et al. (submitted for publication) proposed a B1-GMC criterion. The present paper gives a construction theory and obtains the B1-GMC 2 n − m : 2 r designs with n ≥ 5 N / 16 + 1 , where 2 n − m : 2 r denotes a two-level regular blocked design with N = 2 n − m runs, n treatment factors, and 2 r blocks. The construction result is simple. Up to isomorphism, the B1-GMC 2 n − m : 2 r designs can be constructed as follows: the n treatment factors and the 2 r − 1 block effects are, respectively, assigned to the last n columns and specific 2 r − 1 columns of the saturated 2 ( N − 1 ) − ( N − 1 − n + m ) design with Yates order. With such a simple structure, the B1-GMC designs can be conveniently used in practice. Examples are included to illustrate the theory.