Maximum partial triple systems on 16 and 17 points

It is shown that, up to isomorphism, there are 35 810 097 maximum partial triple systems on 17 points and 47 744 568 maximal partial triple systems on 16 points. It is also established that there are 157 151 non-isomorphic pairwise balanced designs, PBD(17, {3, 5})s, having a single block of size 5. Structural properties of all these systems are determined, including their automorphism groups, and the numbers of Pasch configurations, mitres and Fano planes contained in them. The systems themselves are available from the authors.