That's the crux. What we're saying is that, of these set of ratios, there exists one whose infinite decimal representation contains our intended data. Yes we'd be limited to Planck length resolution, but the idea is that we would determine such a ratio and construct the notch and bar in such a way that it yields the decimal sequence desired; the # of particular ratios is not relevant.

I wouldn't be surprised if it can be proven this can't be done, but then that would be proper question to ask.