Sotiri's Doku Squares

A Doku Square is an \(n \times n\) array containing all integers from \(0\) to \(n-1\) exactly once in each column and each row. The entry in the \(i\)th row and \(j\)th column of Doku Square \(A\) is denoted by \( A_{i,j} \).

We call two \(n \times n\) Doku Squares \(A\) and \(B\) friendly if all \(n^2\) ordered pairs \((A_{i,j},B_{i,j})\) are distinct.

What is the maximum number of \(73 \times 73\) Doku Squares, such that any two of them are friendly?

This problem is shared by Sotiri K.

Details and assumptions

As an explicit example, the two squares \[ \begin{array} { | l | l | } \hline 0 & 1 & 2 \\ \hline 1 & 2 & 0 \\ \hline 2 & 0 & 1 \\ \hline \end{array} \] and \[ \begin{array} { | l | l | } \hline 0 & 1 & 2 \\ \hline 2 & 0 & 1 \\ \hline 1 & 2 & 0 \\ \hline \end{array} \]

are 2 friendly \( 3 \times 3 \) Doku squares.

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