I agree with Andrei here, building hypercubes makes more sense, and feels like it has more structure. It also has the nice property that, once you've seen a (n+1)th element of any range then you have already explored the entire product of the first n elements of every range, kind of like how the colex ordering works.
But which way would you add the successive "shells"? Like this?: (00) (01 10 11) (02 12 20 21 22)... i.e. lex order? btw, what are some real-world uses of the cartesian product of infinite ranges? I can't think of any off the top of my head.
