Classification of flocks of the quadratic cone in PG(3,64)

Flocks are an important topic in the field of finite geometry, with many relations with other objects of interest. This paper is a contribution to the difficult problem of classifying flocks up to projective equivalence. We complete the classification of flocks of the quadratic cone in PG(3,q) for q ≤ 71, by showing by computer that there are exactly three flocks of the quadratic cone in PG(3,64), up to equivalence. The three flocks had previously been discovered, and they are the linear flock, the Subiaco flock and the Adelaide flock. The classification proceeds via the connection between flocks and herds of ovals in PG(2,q), q even, and uses the prior classification of hyperovals in PG(2, 64)

On elation Laguerre planes with a two-transitive orbit on the set of generators

We study finite elation Laguerre planes with a group of automorphisms fixing a generator and acting two-transitively on the set of remaining generators. For odd order, this assumption characterizes the Miquelian Laguerre planes, but there are non-Miquelian examples if the order is even