There are two orthogonal ones of size 4 by 4, and they also exist in a Greco- variety.
These constructs are used in statistical sampling to randomly cover an area with a fixed set of elements. Gaston Terry's proof by exhaustion that there is no solution to the 36 officer problem proved that a more generalized form of them of size 6 by 6 does not exist. Circulent matrices are an example of them, and the Cayley table of a group is one of them. There are two orthogonal ones of size 4 by 4, and they also exist in a Greco- variety. For 10 points, identify this type of n by n array, exemplified by Sudoku, in which each row and column have permutations of the same entries, named by Euler for their traditional use with letters of the namesake alphabet.
These constructs are used in statistical sampling to randomly cover an area with a fixed set of elements.
Latin squares [accept Greco-Latin Squares before "generalized"]