16/12 badminton schedule?

The match between 16 players and 12 players can be played directly in the form of elimination because of the small number of players.

16 matches are suitable for the top four, and all opponents are selected by drawing lots in each round. * * * It takes 16 matches.

12 match is suitable for the top three: the first two rounds draw lots to select opponents, and it takes 9 games to determine the top three. The ranking of the top three is determined by the round robin, which requires three games. * * * Need 12 games.