Steiner almost self-complementary graphs and halving near-Steiner triple systems

We show that for every admissible order v ≡ 0 or 2 ( mod 6 ) there exists a near-Steiner triple system of order v that can be halved. As a corollary we obtain that a Steiner almost self-complementary graph with n vertices exists if and only if n ≡ 0 or 2 ( mod 6 ) .