Experimental design is arguably the most commonly used and effective methodology in scientific investigations and industrial applications. Real-world experiments may have hundreds or even thousands of input variables (factors) and thus a large number of observations (experimental runs) is needed to gain a better understanding of the phenomena under the investigation and estimate the most important parameters without bias and with minimum variance. Constructing optimal designs for these large experiments is a significant NP-hard problem investigators may face. This paper gives a new simple efficient technique, called multiple tripling technique, for constructing optimal (in view of distance, aberration, power moments, orthogonality, uniformity) designs for large experiments with three-level factors by multiple tripling of small and simple three-level initial designs. Some logical questions are now arising, such as how to effectively select initial designs to get optimal resulting multiple triple designs, how to measure the optimality of a resulting multiple triple design relative to all the possible designs with the same size, and what is the efficiency of the multiple tripling technique relative to the existing widely used techniques for constructing large three-level designs? Through theoretical and computational justifications, this paper tries to answer these significant questions. Without computational time (no computer search), the multiple tripling technique is used to construct new recommended optimal designs which are better than the existing recommended designs or cannot be constructed by the existing techniques due to their large sizes.

实验设计可以说是科学研究和工业应用中最常用和最有效的方法。现实世界中的实验可能有数百甚至数千个输入变量（因子），因此需要大量观察（实验运行）以更好地了解所研究的现象并估计最重要的参数而不会产生偏差。最小方差。为这些大型实验构建最佳设计是研究人员可能面临的重大NP难题。本文提出了一种新的简单有效的技术，称为多重三重技术，用于构造最优（鉴于距离，像差，功率矩，正交性，均匀性），将小型和简单的三级初始设计多三倍地用于具有三级因子的大型实验设计。现在出现了一些逻辑问题，例如如何有效地选择初始设计以获得最佳的最终三重设计，如何相对于所有具有相同尺寸的可能设计来测量最终的三重设计的最优性，以及效率如何？相对于用于构建大型三级设计的现有广泛使用的技术，多重三重技术是什么？通过理论和计算依据，本文试图回答这些重要问题。没有计算时间（无需计算机搜索），