How do I improve box and sphere capture reflection quality?

“Due to DX11 hardware limitations, the cubemaps used to capture the scene are all 128 on each side”

Does that mean its 128x128 texture resolution for each plane of a cubemap (6 in total) ? there is really no way to improve it ?

By the way, you seem to be saying that spheres reflection captures are more often the way to go, but I have the feel that if a box reflection capture is used correctly, it can give better results and fake matching up that spheres rc (for having tested it myself)