Some results on constructing two-level block designs with general minimum lower order confounding

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 2^{n ? m}: 2^r designs with 5 × 2^l/16 + 1 ? n ? (N ? 2^l) < 2^{l ? 1} for l(r + 1 ? l ? n ? m ? 1), where 2^{n ? m}: 2^r denotes a two-level regular block design with N = 2^{n ? m} runs, n treatment factors, and 2^r 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.