Matrix with entries from $1$ to $16$, each occuring once, and determinant $40800$

Question

In OEIS, it is claimed, that the largest possible determinant of a $4\ x \ 4$-matrix with the entries from $1$ to $16$, each occuring once, is $40800$.

Unfortunately, the article does not mention a concrete matrix with this determinant.

I tried to find a matrix with turbo pascal, but without success so far.

Can anyone help ?

Answer 1

$$40800 = \det \left( \begin{array}{cccc} 15 & 11 & 5 & 4 \\ 10 & 1 & 14 & 9 \\ 7 & 8 & 3 & 16 \\ 2 & 13 & 12 & 6 \\ \end{array} \right)$$

Answer 2

I just brute force this with Java. I do not think your claim is correct as det({{16, 1, 16, 1}, {1, 1, 1, 16}, {16, 16, 1, 1}, {1, 16, 16, 1}}) = 118125 see:

http://www.wolframalpha.com/input/?i=det%28%7B%7B16%2C+1%2C+16%2C+1%7D%2C+%7B1%2C+1%2C+1%2C+16%7D%2C+%7B16%2C+16%2C+1%2C+1%7D%2C+%7B1%2C+16%2C+16%2C+1%7D%7D%29