A construction of the sporadic Suzuki graph from U3(4)

In this paper, we consider the maximum coclique design of the sporadic Suzuki graph. Then we obtain the 3-(66,16,21) design with the automorphism group U3(4):4. We construct this design as an extension of a 2-design which is described by the 2-transitive action of U3(4) on the 65 isotropic points of the 3-dimensional unitary space over F16. Further, by using this design, we give a new construction of the sporadic Suzuki graph.