I am aware that you can have a balanced solution for 16 players and 30 games of 4 vs 4.
( 5 1 14 9 v 16 7 4 8) ( 3 15 13 6 v 2 10 11 12)
( 6 2 15 10 v 16 8 5 9) ( 4 1 14 7 v 3 11 12 13)
( 7 3 1 11 v 16 9 6 10) ( 5 2 15 8 v 4 12 13 14)
( 8 4 2 12 v 16 10 7 11) ( 6 3 1 9 v 5 13 14 15)
( 9 5 3 13 v 16 11 8 12) ( 7 4 2 10 v 6 14 15 1)
(10 6 4 14 v 16 12 9 13) ( 8 5 3 11 v 7 15 1 2)
(11 7 5 15 v 16 13 10 14) ( 9 6 4 12 v 8 1 2 3)
(12 8 6 1 v 16 14 11 15) (10 7 5 13 v 9 2 3 4)
(13 9 7 2 v 16 15 12 1) (11 8 6 14 v 10 3 4 5)
(14 10 8 3 v 16 1 13 2) (12 9 7 15 v 11 4 5 6)
(15 11 9 4 v 16 2 14 3) (13 10 8 1 v 12 5 6 7)
( 1 12 10 5 v 16 3 15 4) (14 11 9 2 v 13 6 7 8)
( 2 13 11 6 v 16 4 1 5) (15 12 10 3 v 14 7 8 9)
( 3 14 12 7 v 16 5 2 6) ( 1 13 11 4 v 15 8 9 10)
( 4 15 13 8 v 16 6 3 7) ( 2 14 12 5 v 1 9 10 11)
There might be something similar for 18 players and 51 games of 3 vs 3, and 20 players and 38 games of 5 vs 5.
