Enumeration of Nonsingular Buekenhout Unitals


The only known enumeration of Buekenhout unitals occurs in the Desarguesian plane PG(2,q^2).  In this paper we develop general techniques for enumerating the nonsingular Buekenhoutunitals embedded in any two-dimensional translation plane, and apply these techniques to obtain such an enumeration in the regular nearfield planes, the odd-order Hall planes, and the flag-transitive affine planes.  We also provide some computer data for small-order André planes of index two and give partial results toward an enumeration in this case.

DOI Code: 10.1285/i15900932v29n1supplp69

enumeration; Buekenhout unital; nonsingular quadric; translation plane

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