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

We show that for every admissible order v≡0v≡0 or 2(mod6) there exists a near-Steiner triple system of order vv that can be halved. As a corollary we obtain that a Steiner almost self-complementary graph with nn vertices exists if and only if n≡0n≡0 or 2(mod6).