I am not aware of such a relationship between the S/N and posterization, but doubt very much that 256 levels are needed in the brightest f/stop whereas only 70 levels are needed according to the Weber-Fechner law. Look at Norman Koren's link and let me know what you think.
Of course, the number of levels needed to prevent posterization depends on the gamma and fewer levels are need at a gamma of 2.2 than one of 1.0. It is generally accepted that 8 bit gamma 2.2 images are sufficient to prevent posterization in a typical reflection print with a 100:1 luminance ratio.Norman Koren
Even if a given processing of tonal levels leads to a rendering that has posterization that is not visually detectable because it lies under the Weber-Fechner criterion
delta L/L < .01
one can further process the image to make it visible (for instance by simply executing a curves transformation that brings down L leaving delta L fixed). When I wrote that 256 levels (actually it's more like 320) will prevent posterization, I mean that there is no further manipulation of the data that will generate posterization. For specific data transformations such as gamma correction, this may be substantially more than enough, especially in highlights where tonal values are compressed.