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Blocking the inhomogeneous units of experiments into groups is an efficient way to reduce the influence of systematic sources on the estimations of treatment effects. In practice, there are two types of blocking problems. One considers only a single block variable and the other considers multi-block variables. The present paper considers the blocking problem of multi-block variables. Theoretical results and systematical construction methods of optimal blocked  2 n − m designs with  N / 4 + 1 ≤ n ≤ 5 N / 16 are developed under the prevalent general minimum lower-order confounding (GMC) criterion, where  N = 2 n − m .

General Minimum Lower-Order Confounding Designs with Multi-Block Variables