Binary features seem to be very easy to test with solid mathematical limits
Well, I managed to find a paper, and in that paper I saw that someone had a generator for compressing a testing simulation of 100 features each of which had 2 options, down into only 10 tests. Now that got me intrigued, so I spent nearly my entire night laying out combinations and I realized something. One of our combinatorial methods comes into play. I got that from realizing the pattern 4, 10, 20 when I was laying out the possible values of strings 2211, 22211, and 222111.
n = number of tests we are willing to make
m = floor(n/2)
C(n,m) = strings of possible test parameters
n = 10
m = floor(10/2) = 5
C(10,5) = 252
If they are doing it using 10 tests, then we can see there are 252 possible strings at that level. What we need to look for now is how many of those strings are connected pairwise. For instance, a string of 6 tests can represent up to 10 features (1/2 of the total allocated amount). A string of 7 tests can represent 13 to 15 features depending on which set of strings you pick from (I'll come up with a way to determine more features of these strings soon enough). For all even numbered string counts though I believe you can cut the total number of strings in half, and that is the maximum number of testable features.
t = testable features with n tests when even(n) = 0.5*C(n,m)
I'll post a short once I've gotten a chance to work out the odd scenario. I'm thinking it may have something to do with parts, 7 parts of 35 is 5 and 3 of that is 15. The remaining 20, which in turn only have a connection level of 13. It would also formalize the equations so that the m=floor(n/2) makes more sense and further the t equation becomes (m/n)*C(n,m).
References:
[1] http://www.chillarege.com/fastabstracts/issre2003/115-FA-2003.pdf - I'm searching everywhere for existing numbers and I found a couple here.