Abstract Based on an aliased component-number pattern (ACNP), a general minimum lower-order confounding (GMC) criterion has been proposed to choose the optimal regular designs, which minimize the confounding among lower-order effects. This paper is ready to study the properties of GMC s -level designs in terms of complementary sets. It is proved that an s n − m design has GMC only if its complementary set is contained in a flat. Then some GMC s n − m designs are constructed when n = ( N − s r ) ∕ ( s − 1 ) + t and 0 ≤ t ≤ ( s r − s r − 1 ) ∕ ( s − 1 ) , where N = s n − m and r n − m . These results are further illustrated with some examples.

中文翻译：

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构建一些具有一般最小低阶混杂的 s 级规则设计

摘要 基于混叠组件数模式（ACNP），提出了通用最小低阶混杂（GMC）准则来选择最优规则设计，以最小化低阶效应之间的混杂。本文准备从互补集的角度研究 GMC s 级设计的性质。证明了 sn - m 设计只有在其互补集包含在平面中时才具有 GMC。然后当 n = ( N − sr ) ∕ ( s − 1 ) + t 且 0 ≤ t ≤ ( sr − sr − 1 ) ∕ ( s − 1 ) 时，构造一些 GMC sn − m 设计，其中 N = sn − m和 rn - m 。这些结果用一些例子进一步说明。