I would like to perform some black box testing on some software that takes a large number of input variables. These variables can have some interactions (either intentional or non-intentional) so I would like to test a large number of combinations of them and then compare them to the output of another piece of software that is accepted as truth.
Right now I have about 7 3-level variables and about 8 2-level variables, so we talking about half a million runs to do a full factorial test. The software is a little slow, so I'd really like to keep it around the ball park of a few thousand runs.
I'm by no means a statistician and only first heard about design of experiments a week or two ago, so I'm definitely a novice.
I have a few things I can play with to get the number of runs down a decent amount (for example, some variables are only applicable when other variables have certain values) but without some sort of fractional factorial algorithm, I don't think I can get this below 100,000 tests.
My internet searches have yielded plenty of results on 2-level fractional factorial design and I think I mostly get the hang of how that works. But the few pages on multi-level factorial design go way over my head.
Could someone try to explain to me how to create a multi-level factorial design with a somewhat large number of inputs? (Note that I don't care if its a tedious process, because I'm going to write code to do all the busy work for me, I just need to understand the algorithm to create the tests).