On construction of blocked general minimum lower-order confounding 2n−m:2r designs with N/4+1≤n≤5N/16

As an extension of the general minimum lower-order confounding (GMC) criterion to the case of blocked design, a B 1-GMC criterion was proposed (see Wei et al. (2014)). Zhao et al. (2013) constructed all the B 1-GMC 2n−m:2r designs with 5N/16+1≤n≤N−1, where N=2n−m, n and r are the numbers of runs, treatment factors and block factors respectively. In this paper, we establish a construction theory to obtain all the B 1-GMC 2n−m:2r designs with N/4+1≤n≤5N/16. For application, all the B 1-GMC 2n−m:2r designs with N/4+1≤n≤5N/16 and N=16,32,64 and 128 respectively are tabulated.