Extendable Steiner designs

Let D be a Steiner t-design, where t2, with a collection C of subdesigns such that each member of C is a Steiner t-design whose blocks are blocks of D, and with the property that any (t+1) points of D are together in the point set of a unique member of C. It is shown that if every member of C can be extended to a (t+1)-design, then D can also be extended.The construction described is a development of ideas originally formulated in Assmus and Key [2].Dedicated to Professor A. Wagner on the occasion of his 60th birthday