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.