Question: Equally distributed Vectors in Hypercube

I have given a hypercube in dimension d > 3 (in the form (min,max) for each coordinate) and I want to get all integral points in (LaTeX-Pseudo-Code):

Z^d  \cap hypercube

ie. I want to compute all integral coordinates which are in the given boundaries. In d=3 this is easily done by three for-loops. But how in general dimension?

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