Small embeddings for partial triple systems of odd index

AbstractIt has been conjectured that any partial triple system of order u and index λ can be embedded in a triple system of order v and index λ whenever v⩾2u+1, λ(v−1) is even and λ(v2)≡0(mod3). This conjecture is known to hold for λ=1 and for all even λ⩾2. Here the conjecture is proven for all remaining values of λ when u⩾28