The PlayStation Store for PlayStation 3 has been updated to reveal that the file size for the PS3 version of Call of Duty: Black Ops 3 is 17.8GB. As noted, the PS3 version of Black Ops 3 only features the multiplayer and zombies mode, no campaign. (not all features of MP are available, either).
Call of Duty: Black Ops III for PS3 system features two game modes only: Multiplayer and Zombies, providing fans with an expansive Multiplayer and an all-new film-noir inspired Zombies adventure.
Multiplayer provides new ways to rank up, customize, and gear up for battle. Zombies delivers a full-experience experience with its own distinct storyline.
In comparison, the Xbox One file size is around 44.9GB. The file size for PS4 and PC have not been revealed as of now.
SOURCE: PlayStation Store