Finding the ith largest of n for small i,n

A classic problem in computer science is selection: given a list of n numbers, find the ith largest, using the fewest number of comparisons. We are interested in the exact number of comparisons required for specific small values of i and n. We have written a program that can be used either to find the exact number of comparisons for very low values of i and n, or to find upper bounds on the number of comparisons for slightly larger values of i and n. In some cases we have improved on the results in the literature and have additional improvements contingent on a conjecture.