The above argument provides an absolute, rather than only asymptotic lower bound on the number of comparisons, namely comparisons. This lower bound is fairly good (it can be approached within a linear tolerance by a simple merge sort), but it is known to be inexact. For example, , but the minimal number of comparisons to sort 13 elements has been proved to be 34.

Determining the exact number of comparisons needed to sort a given number of entries is a computationally hard problem even for small n, and no simple formula for the solution