According to at least one study, in order to achieve a comparably error-free 3D-LUT to those used for SDR, a LUT size larger than 55x55x55 is required for 12-bit HDR (Rec.2020 ST2084). Of course, such gargantuan LUTs aren’t currently feasible!
“In 10-bit SDR, in order to achieve unnoticeable interpolation errors using the trilinear interpolation method, a 3D-LUT larger than 41×41×41 is necessary. However, using tetrahedral interpolation a 31×31×31 3D-LUT is sufficient. In 12-bit HDR, in order to achieve unnoticeable interpolation errors, a 3D-LUT larger than 72×72×72, is required while a 3D-LUT size of 55×55×55 is sufficient if using the tetrahedral interpolation. The saturated and dark images resulted in a much larger minimum size 3D-LUT to achieve a JND<1 pointing to the possibility that ICtCp is likely not suited for dark images. Further studies are needed with emerging new color difference metrics to evaluate the 3D-LUT size for these types of images. Finally, we determined that reducing the bit-depth from 12-bit to 10-bit will require a 3D-LUT 50% larger on average to maintain a comparable image quality”. – A survey on 3D-LUT performance in 10-bit and 12-bit HDR BT.2100 PQ, JD Vandenberg, Stefano Andriani, SMPTE, 2018