Subsystems of Steiner Systems

Alexander Rosa McMaster University, Hamilton, Ontario, Canada We consider Steiner (n,s,t)-systems with n,s,t natural numbers such that n 2 s > t 2 2. For fixed s , t, a value of n is said to be admissible if n satisfies the necessary condition for the existence of a Steiner (n ,s , t)-system [ 2 ] : ) = integer for i = O,l,..,,t-l. (n-i]/(s-i t-i t-i If there exists a Steiner (n,s,t)-system S define F(n,s,t) to be the smallest integer such that there exists a Steiner (F(n,s,t),s,t) system containing S as a proper subsystem; otherwise let F(n,s,t) be undefined.