The extended binary quadratic residue code of length 42 holds a 3-design

The codewords of weight 10 of the [42, 21, 10] extended binary quadratic residue code are shown to hold a design of parameters 3 − (42, 10, 18). Its automorphism group is isomorphic to P SL(2, 41). Its existence can be explained neither by a transitivity argument, nor by the Assmus-Mattson theorem.