Classification of partitions of all triples on ten points into copies of Fano and affine planes (Q924963)

In two recent papers the authors have studied partitions of the full set of triples chosen from a \(v\)-set into copies of the Fano plane PG(2, 2) or copies of the affine plane AG(2, 3) or copies of both. The Fano partitions for \(v = 8\) and the affine partitions for \(v = 9, 10\) have been fully classified. In the paper under review it is shown that there are precisely 22 isomorphism classes of mixed partitions for \(v = 10\), and it is observed that this completes the classification for \(v\) at most 10. It should be noted that no Fano, affine, or mixed partition exists for \(v\) less than or equal to 7 or for \(v = 11\). For \(v\) greater than or equal to 12 no complete classification seems infeasible.