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A method of tripling for a three-level design, which triples both the run size and the number of factors of the initial design, has been proposed for constructing a design that can accommodate a large number of factors by combining all possible level permutations of its initial design. Based on the link between the indicator functions of a triple design and its initial design, the close relationships between a triple design and its initial design are built from properties such as resolution and orthogonality. These theoretical results present a closer look at a triple design and provide a solid foundation for a design constructed using the tripling method, where the constructed designs have better properties, such as high resolution and orthogonality, and are recommended for application in high dimension topics of statistics or large-scale experiments.