These codes refer to the draw size of various aspects of the tournaments.
For each category of the tournament, the number of participants in the main draw (the main tournament) is listed.
- S: Singles tournament
- D: Doubles tournament
- X: Mixed doubles tournament
For example, at the Rotterdam tournament (32S/16Q/16D/4Q), there were 32 participants in the singles main draw and 16 teams in the doubles tournament.
There are different ways to get into the main draw. Some of the participants are direct acceptances, which means that their ATP or WTA rankings are high enough to get into the main draw directly. Others are wild cards; the tournament organizers have a few spots that they can award to anyone they want. Finally, some spots in the main draws are for qualifiers; these are players who finished at the top of a qualifying tournament that happens before the main tournament. If there is a qualifying tournament for a category, the draw size of the qualifying tournament is listed as "Q" after the main draw size.
In the examples you mentioned:
- Brisbane (28S/32Q/16D)
- Australian Open (128S/128Q/64D/32X)
- Rotterdam (32S/16Q/16D/4Q)
For the 2014 Brisbane International Men's Singles tournament, there were 28 participants in the main draw. Of those 28, 20 were direct acceptances and 2 were wild cards. There was a qualifying tournament held before the main tournament to fill the remaining spots, and there were 32 participants in this tournament. Of these 32, 4 were qualifiers, accepted into the main draw having won their bracket in the qualifying tournament. The remaining 2 places in the main draw were filled by lucky losers, two participants in the qualifying tournament who lost their bracket final, but were still accepted into the main draw due to last minute withdrawals in the main draw.
Brisbane and the Australian Open had no doubles qualifying tournament, but Rotterdam had a small doubles qualifying tournament with 4 teams competing for 1 spot in the doubles main draw. (The runner-up was admitted as a lucky loser.)
The Australian Open is the only one of the three examples that had a mixed doubles tournament; there was no qualifying tournament for this category.