I've been asked to help create a round robin schedule for 32 teams. I think what I want is a Partitioned Balanced Tournament Design. For years, the event has consisted of 40 teams with a prelim day dividing them into two flights where they each play a round robin. Thanks to some tinkering I did with the PBTD(10) posted before, we have a perfect schedule where every team sees every room but one. (Roughly, you just have to interleave the top half and the bottom half and use a different set of rooms for each flight based on the parity of the round number).
Due to COVID issues, the event is likely to have at most 32 teams this year. I created a two-bracket solution with 16 teams apiece as well as a one bracket solution for 30 teams using a (very timely) 2021 paper on ArXiv with a H(15,30) design, but they are now talking the possibility of a 32-team round robin. For the 30 team one, I basically transposed the design so that no team sees any room more than twice and if there are two appearances in a room, they happen in different halves. I believe this is a PBTD(16), but try as I might, I can't find an actual generated one (despite chasing a bunch of literature references that say one exists).
Can anyone help me out here? Unfortunately, time is a bit crunched as I think they need to print the programs on Tuesday.
