Hadamard's maximum determinant problem asks for maximas of the determinant on matrices with entries either -1 or 1.
In this talk, I will introduce a generalisation of this problem for matrices with rows having unit $l_p$ norm. The solution to this problem for small orders will be presented. I will further relate it to the problem of finding Auerbach bases of $l_p$ spaces. Some new results and conjectures on this problem will be discussed.