Pasch trades with a negative block

A Steiner triple system of order v , STS( v ), may be called equivalent to another STS( v ) if one can be converted to the other by a sequence of three simple operations involving Pasch trades with a single negative block. It is conjectured that any two STS( v )s on the same base set are equivalent in this sense. We prove that the equivalence class containing a given system S on a base set V contains all the systems that can be obtained from S by any sequence of well over one hundred distinct trades, and that this equivalence class contains all isomorphic copies of S on V . We also show that there are trades which cannot be effected by means of Pasch trades with a single negative block.