LAUSR

ABSTRACT Block designs are widely used in experimental situations where the experimental units are heterogeneous. The blocked general minimum lower order confounding (B-GMC) criterion is suitable for selecting optimal block designs when the experimenters have some prior information on the importance of ordering of the treatment factors. This paper constructs B-GMC 2n − m: 2r designs with 5 × 2l/16 + 1 ⩽ n − (N − 2l) < 2l − 1 for l(r + 1 ⩽ l ⩽ n − m − 1), where 2n − m: 2r denotes a two-level regular block design with N = 2n − m runs, n treatment factors, and 2r blocks. With suitable choice of the blocking factors, each B-GMC block design has a common specific structure. Some examples illustrate the simple and effective construction method.