Ovals and Hyperovals in Desarguesian Nets

2002/02/12 by David A. Drake, Drake, David A., Kevin Keating +1
Mathematics · #51E14 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:51E14

paper · pdf · doi:10.48550/arxiv.math/0202115

21 pages, LaTeX. We have added a three-page section 6 (with non-existence results). We have also made explicit that ovals of Desarguesian nets are ``affinely equivalent'' under certain assumptions

arxiv created 2002/07/15 · arxiv updated 2009/11/30

Abstract

We determine the Desarguesian planes which hold r-nets with ovals and those which hold r-nets with hyperovals for every r ≤ 7.

Related

• Geometric Hyperplanes: Desargues Encodes Doily
• Pseudo-ovals in even characteristic and ovoidal Laguerre planes
• Nets of conics of rank one in PG(2,q), q odd
• Segre's theorem on ovals in Desarguesian projective planes
• Desargues theorem, its configurations, and the solution to a long-standing enumeration problem