On large sets of disjoint steiner triple systems, IV

Abstract

Let D(v) denote the maximum number of pairwise disjoint Stiner triple systems of order v. In this paper the following theorems are proved: • Theorem 1. If D(1 + 4n) = 4n - 1, n is a positive integer, and p ∈ {1, 2, 5}, then D(1 + 12pn) = 12pn - 1. • Theorem 2. If D(1 + 12n) = 12n - 1, n is an odd number, and p ∈ {7, 11}, then D(1 + 12pn) = 12pn - 1. © 1984.