Excerpt from GNU Emacs manual:

C-u alone has the special meaning of “four times”: 
it multiplies the argument for the next command by four. 
C-u C-u multiplies it by sixteen.
Thus, C-u C-u C-f moves forward sixteen characters.

Is there a way to get this multiplication by sixteen when rebinding universal-argument to a different key? I did the following:

(global-set-key (kbd "C-i") 'universal-argument)

But when I press C-i C-i a only 4 copies of a are inserted, not 16 (if I rebind universal-argument back to C-u then I get 16 copies as advertised in the manual).