Least number not being the determinant of a set of matrices

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Let n > 1 be a natural number and u < v integers. How can I determine the least natural number not being the determinant of some n x n - matrix with integers in the range u..v without calculating simply all the determinants ?

I know that there are upper bounds for the determinant with given size and range of the entries, but how can all the possible values be determined efficiently ?