I have made the following schedule for you where all of a player's partners are different. Also a player will meet all the other players (either as partner or opponent) at least once and at most twice. All players receive exactly 3 bye rounds - although these may not be optimally separated, for example player 14 15 and 16 get two byes in a row.
Week COURT 1 COURT 2 COURT 3 BYES
1 (7 15 v 16 12) (2 6 v 4 5) (3 9 v 11 10) (1 8 13 14)
2 (8 16 v 13 9) (3 7 v 1 6) (4 10 v 12 11) (2 5 14 15)
3 (5 13 v 14 10) (4 8 v 2 7) (1 11 v 9 12) (3 6 15 16)
4 (6 14 v 15 11) (1 5 v 3 8) (2 12 v 10 9) (4 7 16 13)
5 (11 6 v 8 2) (4 12 v 1 13) (16 5 v 9 14) (3 7 10 15)
6 (12 7 v 5 3) (1 9 v 2 14) (13 6 v 10 15) (4 8 11 16)
7 ( 9 8 v 6 4) (2 10 v 3 15) (14 7 v 11 16) (1 5 12 13)
8 (10 5 v 7 1) (3 11 v 4 16) (15 8 v 12 13) (2 6 9 14)
9 (2 3 v 16 13) (5 9 v 15 4) (8 14 v 7 10) (1 6 11 12)
10 (3 4 v 13 14) (6 10 v 16 1) (5 15 v 8 11) (2 7 12 9)
11 (4 1 v 14 15) (7 11 v 13 2) (6 16 v 5 12) (3 8 9 10)
12 (1 2 v 15 16) (8 12 v 14 3) (7 13 v 6 9) (4 5 10 11)
