In this paper we give a necessary condition for the Steiner system \(S(3,4,16)\) obtained from a one-point extension of the points and lines of \( {PG}(3,2)\) to be further extendable to a Steiner system \(S(4,5,17)\).
Citation
Alphonse Baartmans, Joseph Yucas. On the Existence of a Double Extension of PG\((3, 2)\)[J], Ars Combinatoria, Volume 033. 146-157. .