Li et al. (Comm Statist Theory Methods 49: 924–941, 2020) introduced the concept of inverse Yates-order (IYO) designs, and obtained most of two-level IYO designs have general minimum lower-order confounding (GMC) property. For this reason, the paper extends two-level IYO designs to three-level cases. We first propose the definition of \(3^{n-m}\) IYO design \(D_q(n)\) from the saturated design \(H_q\) with three levels. Then, the formulas of lower-order confounding are obtained according to the factor number of \(3^{n-m}\) IYO design: (i) \(q<n<3^{q-1}\), and (ii) \(3^{q-1}\le n\le (N-1)/2\), where \(N=3^{n-m}\). Under case (ii), we obtain the explicit expressions of lower-order confounding for four structure types of IYO designs. Some examples are given to illustrate the theoretical results. Compared with GMC designs, three-level IYO designs with 27- and 81-run are tabulated to show that some of them have GMC property through lower-order confounding.

李等人。(Comm Statist Theory Methods 49: 924–941, 2020) 引入了逆 Yates-order (IYO) 设计的概念，得出大多数二水平 IYO 设计具有一般最小低阶混杂 (GMC) 属性。为此，本文将两级 IYO 设计扩展到三级案例。我们首先从三个层次的饱和设计\(H_q\)中提出\(3^{nm}\) IYO 设计\(D_q(n)\)的定义。然后，根据\(3^{nm}\) IYO设计的因子个数得到低阶混杂公式： (i) \(q<n<3^{q-1}\)，和 ( ii) \(3^{q-1}\le n\le (N-1)/2\)，其中\(N=3^{nm}\). 在情况（ii）下，我们获得了 IYO 设计的四种结构类型的低阶混杂的显式表达式。给出了一些例子来说明理论结果。与 GMC 设计相比，将具有 27 次和 81 次运行的三水平 IYO 设计制成表格，以表明它们中的一些通过低阶混杂具有 GMC 特性。