User:Jeremydover/sandbox/Hall plane of order 9

Construction
This plane can be constructed from a Hall quasifield with defining polynomial $$f(x) = x^2 - \omega$$, where $$\omega$$ is a primitive element of $$GF(9)$$.

This plane can be constructed using the André/Bruck-Bose construction with a regular spread of $$PG(3,3)$$ that has had a single regulus replaced by its opposite.

Ovals and Hyperovals
This plane has odd order, so by Qvist's theorem it does not have a hyperoval. It does have ovals.

Subplanes
The Hall plane of order 9 has subplanes of orders 2 and 3.

Unitals
It has several unitals.