Uniqueness of the inversive plane of order sixty-four
In this paper, the author classifies ovoids in \(\mathrm{PG}(3,64)\) as elliptic quadrics. The author starts with a nice historical overview of some main results leading up to this classification. The computer techniques used are similar as in the paper of \textit{C. M. O'Keefe} et al. [J. Geom. 50, No. 1--2, 143--150 (1994; Zbl 0805.51004)] which dealt with the classification of ovoids in \(\mathrm{PG}(3,32)\). There are several corollaries for related concepts in finite geometry. Most notably, it follows that there is a unique inversive plane of order 64. Further consequences for generalised quadrangles and translation planes are described in the last section.
scientific article; zbMATH DE number 7494016
scientific article