Mixed partitions of sets of triples into small planes Original Research Article

We continue our study of partitions of the set of all (v3) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2,2) and copies of AG(2,3), and deal with the cases v=13,14,15 and 17. These partitions, together with those already known for v=12,16 and 18, then become starters for recursive constructions of further infinite families of partitions.