Courtsey of Professor Brendan McKay:

There are:
* 355,293,682  3-(32,16,7) designs
* 10,374,196,953  2-(31,15,7) designs
* 6326348471771854942942254850540801096975599808403992777086201935659972458534005637120000000000000 Hadamard matrices altogether (not considering equivalence)