We construct by computer all of the hyperovals in the 22 known projective planes of order
16. Our most interesting result is that four of the planes contain no hyperovals, thus providing …

In each of the three projective planes coordinatized by the Knuth's binary semifield K n of
order 2 n and two of its Knuth derivatives, we exhibit a new infinite family of translation …

The conics of a finite Desarguesian plane of square even order satisfying the following
properties are classified.(1) Their two infinite points (one being the nucleus) do not intersect …

The Hall plane of order q2 is constructed from the Desarguesian plane of order q2 by the
process of derivation with respect to a fixed derivation set on a fixed ideal line. The affine …

Translation Laguerre planes of order 16 are investigated, and a related search is carried out
for translation ovals in the eight translation planes of order 16 and for certain collections of …

A Kakeya set 𝓚 in an affine plane of order q is the point set covered by a set 𝓛 of q+ 1
pairwise non-parallel lines. By Dover and Mellinger, Kakeya sets with size at least q 2–3 q+ …

There are many open problems concerning strongly regular graphs: proving non-existence
for parameters where none are known; proving existence for parameters where none are …

In this note we complete the classification of inherited hyperconics in Hall planes of even
order that was started by O'Keefe and Pascasio by proving that in the cases left open in [CM …

Let C¯ be a conic in PG (2, q2) and suppose we derive with respect to a derivation set or
multiple derivation set. This paper looks at whether the conic C¯ gives rise to an inherited …

The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian
planes. The aim of this paper is to describe when a conic of PG (2, q) remains an arc in the …