Generating counterbalanced orders

Solution

The function (defined below) can be used to generate Latin squares.

Once you generate your Latin squares, it is a good idea to inspect them to make sure that there are not many duplicated sequences. This is not uncommon with smaller squares (3x3 or 4x4).

Testing the function for randomness

Some algorithms for generating Latin squares may not create them very randomly. There are 576 unique 4x4 squares, and each one should have an equal probability of being created, but some algorithms do not properly do this. There is probably no need to test the randomness of the function above, but here is some code that will do it. Previous algorithms that I used did not have a good random distribution, which was discovered by running the code below.