Taguchi developed a series of arrays, often referred to as Taguchi Orthogonal Arrays, for use with Taguchi Designs. These are designated Ln arrays, where 'n' is the number of treatments.
The columns in these arrays are highly confounded. They are generally used as screening designs, with only selected interactions investigated. The arrays include two, three, four, and mixed level designs.
Taguchi developed a system of Linear Graphs to help allocate factors to the columns in the arrays.