https://www.gamespot.com/articles/call-of-duty-black-ops-4-has-50-gb-day-one-update/1100-6462396/

Call of Duty: Black Ops 4 is going to take a healthy chunk of hard drive space when it installs from the disc, but you'll need to keep some space open for the day-one patch as well. Depending on your console of choice, you should have as much as 112 GB of free space to complete the installation.

According to Activision's support page, the day-one update has a download size of 50 GB, and when it's all done the game will leave a 55 GB footprint on your PlayStation 4 or Xbox One. On PlayStation 4 you'll need to have more room set aside, though, as it states that for an "optimized download experience" you'll want 112 GB of free hard drive space. This is just the size needed to complete the installation, though, and once the process is complete it will go back down to the 55 GB requirement.