3 person tournament with no repeats, 16 players

[simpsong00]

I'm trying to devise a tournament with the following criteria.

1) 16 players
2) 3 person teams, 2 teams play against each other
3) Each player only plays with each other player 1 time.
4) 2 matches each week for 8 weeks, allowing each player 2 bye weeks. 

Something like this, only for 8 weeks... I simply brute forced it for 6 weeks, but couldn't get week 7 or 8... So, I'm searching for an algorithmic way to do it...

Any thoughts appreciated.

[Ian Wakeling]

Consider looking for a cyclic solution where the problem reduces to finding a suitable first round from which the other rounds can be generated.

Doing this I have found the schedule below which I think meets your criteria, but the balance of opposition pairs is relatively poor - there are about 20 or so pairs of players who never oppose.

   (1 2 10 v 12 14 15) (4 7 11 v 3 5 16) [6 8  9 13]
   (2 3 11 v 13 15 16) (5 8 12 v 4 6  9) [7 1 10 14]
   (3 4 12 v 14 16  9) (6 1 13 v 5 7 10) [8 2 11 15]
   (4 5 13 v 15  9 10) (7 2 14 v 6 8 11) [1 3 12 16]
   (5 6 14 v 16 10 11) (8 3 15 v 7 1 12) [2 4 13  9]
   (6 7 15 v  9 11 12) (1 4 16 v 8 2 13) [3 5 14 10]
   (7 8 16 v 10 12 13) (2 5  9 v 1 3 14) [4 6 15 11]
   (8 1  9 v 11 13 14) (3 6 10 v 2 4 15) [5 7 16 12]

I think it likely that other schedules with better opposition balance exist.

[simpsong00]

Thank you very much. This is extremely helpful.