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In this paper, we enumerate the (nonisomorphic) Steiner triple systems of order 19 which contain a subsystem of order 9. The number of these designs is precisely 284457. We also determine which of these designs also contain at least one subsystem of order 7, and how many. Exactly 13529 of them contain at least one subsystem of order 7.

284457 Steiner triple systems of order 19 contain a subsystem of order 9