Designs from maximal subgroups and conjugacy classes of Ree groups

Abstract

In this paper, using a method of construction of \begin{document}$ 1 $\end{document} -designs which are not necessarily symmetric, introduced by Key and Moori in [ 5 ], we determine a number of \begin{document}$ 1 $\end{document} -designs with interesting parameters from the maximal subgroups and the conjugacy classes of the small Ree groups \begin{document}$ ^2G_2(q) $\end{document} . The designs we obtain are invariant under the action of the groups \begin{document}$ ^2G_2(q) $\end{document} .