The elementary Abelian Steiner systems S(2,4,49) (Q579267)

A Steiner system S(t,k,v) is a t-design with parameters (v,k,1). A Steiner system is said to be elementary Abelian if it has an elementary Abelian collineation group of order v acting transitively on the v points. It is known [\textit{T. Beth, D. Jungnickel} and \textit{H. Lenz}, Design Theory (1985; Zbl 0569.05002)] that there are exactly 224 cyclic S(2,4,49). The author shows that there are 12 non-isomorphic elementary Abelian S(2,4,49), all distinct from the cyclic S(2,4,49).