Here are some linearity measurements I've done on a March DAC 1. With lower noise levels you can see further down in level.
First is a spectrogram of the lower bits. I used a 12 khz tone so that only one bit level is turned on at any time. I've marked the bits. The spectrogram is set so that the background goes light gray at -152 dbFS. Using a 32 k FFT pushes the noise floor down below this so the test tone can stand out. The vertical bars are just markers.
Next is a table where I exported the 64K FFT results to a spreadsheet. You see the value at 12,000 hz and beside it the target value for each bit level. As you see these results are not far at all from what you are hoping to see. The 24th bit is less than half a db off in level and the others are less than .1 db off in expected level.
To get these results I made up a signal with these very low level tones. Sent it from the DAC into the microphone inputs of a recording interface. Used the gain of the microphone input to boost levels above the intrinsic noise floor of the interface. I then took the recorded result and adjusted a reference -60 db tone I had embedded so that is was at -60 dbFS again. Which should put all the other signals at their true level leaving the DAC. This seems to work well to separate noise from the tone levels coming from the DAC.
My tests of various sigma delta DACs indicates they get linearity correct until noise obscures the results. Likely they are putting out the signal correctly below the noise.