Note: The generating rank of the U4(3) near hexagon

AbstractYoshiara [Embeddings of flag-transitive classical locally polar geometries of rank 3, Geom. Dedicata 43 (1992) 121-165] and Bardoe [On the universal embedding of the near-hexagon for U"4(3), Geom. Dedicata 56 (1995) 7-17] showed that the embedding rank of the U"4(3) near hexagon E"3 is equal to 21. The precise value of the generating rank of E"3 has been unknown, see Cooperstein [On the generation of some embeddable GF(2)-geometries, J. Algebraic Combin. 13 (2001) 15-28]. In this note, we determine this generating rank. We give a short proof for the fact that the generating rank and the embedding rank of E"3 are equal to 21.