John Bamberg, Michael Giudici, Gordon F. Royle
Published 2010-12-17, updated 2011-10-06Version 3
In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order $(5^2,5)$ and give numerous further examples of hemisystems in all the known flock generalized quadrangles of order $(s^2,s)$ for $s \le 11$. By analysing the computational data, we identify two possible new infinite families of hemisystems in the classical generalized quadrangle $H(3,q^2)$.
Comments: slight revisions made following referee's reports, and included raw data
Unifying the known infinite families of relative hemisystems on the Hermitian surface
Infinite families of 2-designs from GA_1(q) actions
Infinite families of $2$-designs from a class of linear codes related to Dembowski-Ostrom functions
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