Reshuffle group combinations without repitition...

That's where the complexity and the limitation's of the formulas come in. there are too many variables/flags that would have to be checked by a formula so that a schedule would go as long as it could before repeating.

The formula/macro/program would have to lets say for player 1.
Would not only have to check who he played with all previous weeks and eliminate those that he played with, it would have to then check the players left to see who they played with and eliminate the players they already played with and so on till your left with only those who have never played together and put them in for that week. plus it would have to check who has already been used for another team.

Example:
Week 1-
Team 1 players are 1-2-3-4
Team 2 players are 5-6-7-8
Team 3 players are 9-10-11-12
and so on.

Week 2-
Team 1 players are 1-5-9-13
Why these numbers? Because:
player 1 cant play with 2-3-4 because they played together already next available number is 5
player 5 cant play with 6-7-8 because they played together already next available number is 9
player 9 cant play with 10-11-12 because they played together already next available number is 13

Team 2 players are 2-6-10-14
here it had to also check team 1 to eliminate 5-9-13 because they are being used by team 1.

So you see there would be a lot of cross referencing numbers that would have to be done.

But then at some point its going to start repeating.

24 players in 6 groups of 4 players playing once a week. can go I think about 7 weeks before somebody has to play with someone they played with before.

Now a couple of people have said you might could do it with a database, but I've never seen one or a example and I don't about making databases.