In this paper, it is shown that there are exactly \(5\) non-isomorphic abstract ovals of order \(9\), all of them projective. The result has been obtained via an exhaustive search, based on the classification of the \(1\)-factorizations of the complete graph with \(10\) vertices.
Citation
Massimo Giulietti, Elisa Montanucci. Abstract Ovals of Order \(9\)[J], Ars Combinatoria, Volume 091. 297-301. .