ffmpeg – Loop video to audio without increasing it’s file size

Does any modern codec/container support looping video for certain amount of time/cycles?

What I’m trying to achieve, is I have a small 15 second video file and a 3 minute audio file, and I want to loop video while audio is playing, but without encoding the video over and over.

Making something similar to what you can see https://coub.com site, but just using some native codec/container technique, as that websites stores the gif and mp3 separately.
Is it possible?