Embedding Steiner triple systems into Steiner systems S(2,4,v)

We initiate a systematic study of embeddings of Steiner triple systems into Steiner systems S(2,4,v). We settle the existence of an embedding of the unique STS(7) and, with one possible exception, of the unique STS(9) into S(2,4,v). We also obtain bounds for embedding sizes of Steiner triple systems of larger orders.