Hemisystems of small flock generalized quadrangles

In this paper, we describe a complete computer classification of the hemisystems in the two known flock generalized quadrangles of order (5, 5) and give numerous further examples of hemisystems in all the known flock generalized quadrangles of order (s, s) for s 6 11. By analysing the computational data, we identify two possible new infinite families of hemisystems in the classical generalized quadrangle H(3, s).