Enumeration of Balanced Tournament Designs on 10 Points

We enumerate the balanced tournament designs on 10 points (BTD(5)) and find that there are exactly 30,220,557 nonisomorphic designs. We also find that there are exactly two nonisomorphic partitioned BTD(5)’s and 8,081,114 factored BTD(5)’s on 10 points. We enumerate other classes of balanced tournament designs on 10 points and give examples of some of the more interesting ones. In 1988, Corriveau enumerated the nonisomorphic BTD(4)’s, finding that there are 47 of them. This paper enumerates the next case and provides another good example of the combinatorial explosion phenomenon.