Doubly Orthogonal Equi‐Squares and Sliced Orthogonal Arrays

ABSTRACT We introduce doubly orthogonal equi‐squares. Using linear algebra over finite fields, we produce large families of mutually ‐doubly orthogonal equi‐ squares, and show these are of maximal size when . These results specialize to the results of Xu, Haaland, and Qian when and the equi‐squares are Sudoku Latin squares of order . Further, we show how a collection of mutually ‐doubly orthogonal equi‐ squares can be used to construct sliced orthogonal arrays of strength two. These orthogonal arrays have important applications in statistical designs.