Derived Steiner Triple Systems of Order 15

Abstract

A Steiner system is denoted by S ( t, k, ν ) where the parameters have their usual meaning. It is an elementary proposition that if any point of a Steiner system is chosen, all blocks not containing the point are deleted, and the point itself is then deleted from all of the remaining blocks, what remains is another Steiner system S ( t-1,k-1, ν-1 ). Such ν are called “admissible.” It follows that there exists a derived Steiner triple system for every admissible order. However, whether or not every Steiner triple system is derived is a fascinating open question. A Steiner triple system of order 2 ν + 1 with a derived Steiner triple system of order ν is itself derived.