An extension theorem for Steiner systems Original Research Article

Given a Steiner system S(2, k–1; v) with v ⩾ vo(k), there is a 3-design Sλ(3, k; v + 1) such that the derived design is λ copies of the Steiner system for any λ sufficiently large satisfying the standard arithmetic conditions. This theorem has applications in the construction of Steiner 3-designs.