And here's a 36er. 

ELQV AEPR IKNR FHTW BEIS DFMQ CQRX CGJV DOPX FGSX BDHR MNWX GKLP ABCT 
+EHNU JMST EFKO BFLN AJOW ADGU BPVW AKMV AHIQ IMPU KQUW CHPS NPQT CDEW
+ DIJL GMOR TUVX LRSW DNSV CLOU FJRU BJKX

[download]

I've found it by randomly adding new teams until the set was maximal, starting from no teams repeatedly until it got larger than 35.

J source (modified from the above post; to see how slow it works, it prints the number of teams in a set it's found after each try): 

   players =: a.{~65+i.24
   teams =: (#~]-:"1~."1)~./:~/:~"1>,{4$<players
   good =: teams#~[:(*./"1) 1>: teams&(+/@:e."1"1 _)
   fmt =: ,/@:(,&' '"1)"2
   rand =: 3 :'((,(?@:#{])@:good) ::])^:_ i.0 4'
   fmt 3 :('while. 1!:2&2#(t =: rand 0)'; '35>:#t'; 'do. end.'; 't') 0

[download]

Update: I got lucky. Here's a set of 38 teams (generated using the same code except by raising the constant 35). 

BEHN KQTX BJMR GIPQ ELTW DNPV AGHU GLMO JNOT CEFI KOSW ADMX AJVW CLPU 
+AFLS HJSX DIOU BFGK FOPR BDQS CHQW HIKM ACKN KLRV NRSU FHTV EGRX CDGT
+ EMUV MPST FJQU EJKP FMNW BPWX COVX AEOQ ILNX ABIT

[download]

In reply to Re: Unique Combos with Math::Combinatorics by ambrus
in thread Unique Combos with Math::Combinatorics by ketema

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