The mirror image of the biggest-number puzzle asks a subtler question: build the minimum. Ascending order puts the smallest digit first, but a leading zero secretly erases a whole digit - 0149 is just 149 - so the true smallest arrangement must start with the smallest nonzero digit and only then let zeros in.
Generate the Smallest Number handles that rule for you. Arrange a full digit set into its minimum, or fix a length and a pool and let each position take the smallest allowed digit. The result prints exactly, grouped on request, ready to copy or download.