I have 24 classes of sets of 6 elements each.
For example: (a1, a2, a3, a4, a5, a6), (b1, b2, b3, b4, b5, b6)... (x1, x2, x3, x4, x5, x6).
Altogether, there are 24*6= 144 elements.
I am trying to create 36 unique combinations of 4 elements (144/4=36). For example, (a1, b1, c1, d1). The same class must not be repeated in a same combination. For example, (a1, a2, b1, c1) would not be acceptable. Once an element has been used in a combination, it cannot be used further.
To further complicate things, I am hoping to minimize the number of times that different classes are paired in the same combination. For example, if my first combination is (a1, b1, c1, d1), I'd like to avoid pairing "a" elements with "b", "c", and "d" (and b with c and d, and c with d) in my other combinations as much as possible.
Is this possible? Or am I doomed to have certain pairs repeat a certain number of times. I've tried multiple ways of creating my combinations by hand but it gets really complicated when I get about half way. Is there a systematic way of doing this?
Edit:also, what if I have a different number of classes, and number of elements therein. Is there an approach I can use to solve this sort of problem?