title: Results for Two-Level Designs with General Minimum Lower-Order Confounding.
abstract: The general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pattern (AENP). Therefore, it is very important to study properties of AENP for two-level GMC design. According to the ordering of elements in the AENP, the confounding information between lower-order factor effects is more important than that of higher-order effects. For two-level GMC design, this paper mainly shows the interior principles to calculate the leading elements 1 (#) C 2 and 2 (#) C 2 in the AENP. Further, their mathematical formulations are obtained for every GMC 2 (n-m) design with N = 2 (n-m) according to two cases: (i) 5N/16 + 1 ≤ n < N/2 and (ii) N/2 ≤ n ≤ N - 1.
authors.affiliation: School of Mathematical Sciences, Xinjiang University, Urumqi 830046, China.
authors.forename: Zhi Ming
authors.initials: ZM
authors.lastname: Li
authors.affiliation: KLAS and School of Mathematics, Northeast Normal University, Changchun 130024, China ; LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, China.
authors.forename: Run Chu
authors.initials: RC
authors.lastname: Zhang