# Constructing finite projective planes

## J. B. Nation, University of Hawaii

## October 10, 2017

A semiplane is a collection of lines such that every
pair of lines intersects in a unique point. Semiplanes provide
a natural starting point for computer searches to find projective
planes with certain properties, e.g., planes of non-prime-power
order.

A non-desarguean configuration can generate 845 distinct semiplanes,
which fall into 105 isomorphism classes. Of these, 15 are minimal in
the sense that every non-desarguean plane must contain one of these
semiplanes.

This is joint work with Jiajia Seffrood.