32 starters, 4 qualifiers

(5 wins needed for qualification, 2 defeats for dropping out):

Double line: dropped out,
* One of them still qualifies,
Those in bold red: qualified.

Explanation: In each round every team gets an opponent from its category. After the fifth round there will be one (5/0) (a qualified team), five (4/1), four (3/2) and this is where the 6th point of the basic rules should be applied. One of the four latest drop-outs will still qualify by getting re-grouped as the sixth of the so far five-member (4/1) group.
In the fifth round the eight (3/1) teams played knowing that besides the four winners one more of them will still qualify. There are two ways to avoid the abuse of the system:
        1. It is not the best of them who automatically gets selected, but the best and the second best play an extra match. Therefore it is not for sure that the best loser gets qualified and it is not worth playing for a defeat.
        2. The organisers do not reveal in advance the method of choosing the best loser, but define several methods, for example
          - the biggest goal difference,
          - the most goals shot,
          - the least goals got,
          - best result quality,
          - hardest opponents.
The organisers draw from these subsequent to the matches and decide upon an order of importance. It is practically impossible for any team to be able to predictably fulfil all these criteria as the best, especially if some matches are played simultaneously.
Thus, after the fifth round a team (5/0) has already qualified and they stop playing in this round, and after the sixth round there will be three more (5/1) teams who also have qualified to the next round and three teams (4/2) who have dropped out.
This way a competition with 32 participants can be enjoyed all through, as on each match each group has the same at stake.
Note: The football world cup has now 32 participants and 64 matches, while in this system, there would be 62 or 63 matches.