Sorting combinations of linearly independent vectors

Question

Given a set of $m$ vectors in $\mathbb{R}^n$ ($m > n$), sort all combinations of $n$ linearly independent vectors according to the determinant of the matrix whose columns are the $n$ vectors. Obviously it is possible to do this in a brute force way, but I am looking for a systematic method to generate the next smallest combination without enumerating the entire space of $m \choose n $ combinations.