3 research outputs found
Nonexistence Certificates for Ovals in a Projective Plane of Order Ten
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.Comment: Appears in the Proceedings of the 31st International Workshop on
Combinatorial Algorithms (IWOCA 2020