Reshuffle group combinations without repitition...

This is an individual movement from duplicate bridge -- maybe it can be adapted to 16 rounds for 24 players.

      -A- B- -C- -D- E F- -G- -H- I- J -K- -L- -M- -N- O -P- Q- -R- -S-
  1   16  1   6  10    4   5  13  3     8  15  12   9     7  2  11  14 
  2   16  2   7  11    5   6  13  4     9  15   1  10     8  3  12  14 
  3   16  3   8  12    6   7  13  5    10  15   2  11     9  4   1  14 
  4   16  4   9   1    7   8  13  6    11  15   3  12    10  5   2  14 
  5   16  5  10   2    8   9  13  7    12  15   4   1    11  6   3  14 
  6   16  6  11   3    9  10  13  8     1  15   5   2    12  7   4  14

As spreadcore says, this is, in general, a very hard problem.

Heres a quick try for you to see if this is close to what your looking for.

Its 24 players divided into 6 groups of 4 players each week for 20 weeks. Using a variation of the above formulas.