According to an answer on stack exchange, the minimum number of pairwise combinations is 9. The concept of pairwise combination takes any 2 parameters at a time, and doesn't care about the rest. The trivial solution to the example is:
- dim1.small x dim2.small x dim3.small
- dim1.small x dim2.medium x dim3.medium
- dim1.small x dim2.large x dim3.large
- dim1.medium x dim2.small x dim3.medium
- dim1.medium x dim2.medium x dim3.large
- dim1.medium x dim2.large x dim3.small
- dim1.large x dim2.small x dim3.large
- dim1.large x dim2.medium x dim3.small
- dim1.large x dim2.large x dim3.medium
We have every possible value pair you could draw from any pair of parameters, but we do not have every unique triplet (that would be the "exhaustive" approach, and result in 3x3x3 = 27 combinations).
I still have no idea where 10 comes from in the documentation example.