1080p quality with low bitrate

Bitrate is large part of file size, I've posted many time before trying to find a way to keep the 1080p quality with a small file size but now I realize thats almost impossible. I was shown a bite rate calculator that help give the bitrate to use tp obtain certain file sizes. Now I see it the type of encoding that is used to help keep the high Bluray 1080p quality. As always with lowering the bite rate which lowers the file size that ultimately lowers the quality. Screen is not as bright as true Blu ray, true black not as dark with other aspect unknown to me.

Is H.264 the best for encoding blu ray to keep the high qulity of blu ray with low file size.