What is the maximum value of the $4 times 4$ determinant composed of 1-16?

If 1-9 is filled in the $3 times 3$ determinant, and each number appears once,then the maximum value of the determinant is $412$.

For example, the following determinant can take the maximum value of $412$:
$$left|
begin{array}{ccc}
1 & 4 & 8 \
7 & 2 & 6 \
5 & 9 & 3 \
end{array}
right|=412.$$

Question: if 1-16 is filled in the $4times4$ determinant, and each number appears once, what is the maximum value of the determinant? Is it necessarily less than $16 times 15 times 14 times 13= 43680$?