orthogonal array

In mathematics, orthogonality is a generalization of perpendicularity. For vectors, it means their dot product is zero. For functions, it means the definite integral of their product is zero. A set of orthogonal elements can form a basis for a space, meaning any element can be created from a combination of these basis elements.1

Orthogonal arrays are a concept in combinatorics, introduced by C.R. Rao. An orthogonal array is a matrix where specific submatrices contain all possible column vectors with equal frequency. These arrays are related to orthogonal Latin squares and are used in factorial designs, where treatments combine factors at different levels. They also have applications in communication theory and the construction of error-correcting codes.2