I don't know of any way to build a ladder DAC where the absolute and relative precision of the resistors wouldn't matter. It seems to me as if the concept for the Ring DAC was originally born out of the technical feasibility to overcome what is ultimately a manufacturing problem. Needless to say, laser-etching has been improved etc. (one of my friends is an engineer in chip design, who'll occasionally educate me on the latest developments), but it appears there are technical limitations.
Greetings from Switzerland, David.
Different ladder DACs are built to different specifications of precision and measure differently. The four expensive precision AD5791 DAC chips in my Schiit Yggdrasil OG DAC (Yggdrasil Analog 2 DAC) apparently have very good DNL (differential non-linearity) and INL (integral non-linearity) measurements:
(For the suggested precision applications, see there.)
As stated its operation is guaranteed monotonic, the importance of which is explained in this link about DNL and INL:
The designer of the DAC (Mike Moffat, formerly Theta Digital) chose this precision DAC chip for its linearity, even though it has a zero-crossing glitch energy problem and thus is not recommended for audio applications by the manufacturer (he solved the glitch energy problem in his DAC circuitry; a 1kHz sine wave at -90 dB measures perfectly). He says most audio ladder DAC chips have such bad linearity that the measurements are not even listed in the data sheets (a cursory check by me of a few data sheets for some widely used audio ladder DAC chips seems to bear out such lack of linearity measurement listings).