4K can be done at less than Blu-Ray bitrates. ATSC broadcasts are roughly 18.3 Mbps after overhead is taken into account, and that's typically MPEG-2. h.265 can produce the same perceptual quality (measured by PSNR) at about 5.5 Mbps. If you go for a simple quadrupling of bitrate to account for the quadrupling of pixels, you'd get equivalent ATSC quality (pixel for pixel) for 4K video at about 22 Mbps.
In practice, however, bitrate and pixel counts don't scale in lockstep like that. If you double the number of pixels, you don't need to double the bitrate. There are a variety of reasons for that. For one thing, as resolution increases, the compression artifacts shrink (in real-world size, not pixel-size), making it harder to discern them. For another thing, there's only so much detail in an image, and resolving a low-detail area in higher resolution might not require any extra bits at all.
I don't have any numbers to say what the reduction would be... but in any case, the point is that decent looking 4K video can be done at substantially lower bitrates than blu-ray supports. Of course, in practice, blu-ray movies use substantially lower bitrates than blu-ray supports anyhow, so I suspect it would come out in the wash.--
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