This is the method I used to level an entire prestige (35 levels) in just one day of play! That's approximately 14,000 kills in a single day of playing, and I did it without dying to the hordes of undead.
You don't need to be a good player to follow this strategy. Thanks, in part, to the fact that you won't be killable while doing this!
Watch the video and see how you can powerlevel the fastest way possible in Black Ops 3 Zombies.