Lexicographic ordering of the sets X and Y is crucial in the problem described in the post because it admits an efficient algorithm for iterating through X*Y wi

Lexicographic ordering of the sets X and Y is crucial in the problem described in the post because it admits an efficient algorithm for iterating through X*Y without needing to enumerate them prior. It would not work for e.g. binary-on-disk ordering, since algebraic laws don't carry over in that ordering.