Nonexistence Certificates for Ovals in a Projective Plane of Order Ten

Abstract

In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no nonexistence certificates were produced by this search, and to the best of our knowledge the search has never been independently verified. In this paper, we rerun the search for ovals in a projective plane of order ten and produce a collection of nonexistence certificates that, when taken together, imply that such ovals do not exist. Our search program uses the cube-and-conquer paradigm from the field of satisfiability (SAT) checking, coupled with a programmatic SAT solver and the nauty symbolic computation library for removing symmetries from the search.