It's certainly possible to imagine universes in which that would work. But in ours, where stuff is made of atoms, I can't see you positioning the mark on the r

It's certainly possible to imagine universes in which that would work. But in ours, where stuff is made of atoms, I can't see you positioning the mark on the rod any more precisely than the width of an atom, which I think is about 10 to the -10 meters. So I'm guessing you could only encode 30 or 40 bits, even with super-advanced etching and measuring equipment.