Sorting algorithms

[Era Scarecrow]

 Been watching online lectures that's going into sorting and 
searching, and from what I'm seeing most sorting algorithms (by 
using comparison; merge sort, quicksort, etc) and even tree 
algorithms peak at O(n log n). So an example area to be sorted 
with 16 elements would take on average about 100 compares while 
theoretically you can do it in half that number.

 What algorithms get you closest to that optimal value? If there 
isn't any I have an idea that may just do it. Either way I'll be 
trying to implement it and see how it performs.

 I wonder what happens if I succeed and become famous... O.O