One No Man's Sky player has managed to build a Mass Relay from Mass Effect in orbit of a planet, using over 2,900 parts. It's an incredibly impressive feat that uses some equally as impressive trickery to work.
There are a few techniques to build bases in a planet's atmosphere — YouTuber Beeblebum has an entire video on the topic that goes into much more depth — but to give you a brief idea of how it works, I'll break down the most commonly used method.
Place a base computer on the ground and then save the game manually at your ship so that you can reload if something goes wrong. Then build 315 walls into the air and snap a landing pad to the top. Trigger an autosave by running around and reload the game via that autosave to see if the walls and, most importantly, the landing pad are still in place.
Afterwards, fly to the landing pad and build a second base computer — you can then place more walls and repeat the autosave trick to see your build limit. Once you're ready, pick up the base computer and move it into the air. Doing this allows you to...