Like several others, when I lauched the game earlier today I found that BO3 indicated the NAT as initially showing Moderated. I terminated the game and re-started it hoping that would fix the problem, but instead it now changed the NAT type to "Strict".
In order for the game to show NAT as open, I ended up having to restart the PS4 and also the R1. Following that, all is well and NAT now shows as Open.
Also - a wierd quirk about this game (until they resolve it) is that when you try to play multiplayer, if you happen to hit "X" to continue immediately following the opening intro thing, it'll fail and you'll not be able to play online. The way around this is to be patient and wait until the top right of the screen changes from 33.0.0 whatever to 220.127.116.11 (or something equivalent) and THEN hit "x" to continue. Once you do this, online gameplay works fine
[ Reposting into this new thread per recommendation from one of the moderators. Posted here earlier. Perhaps this thread can be made sticky ]