Constructions of disjoint Steiner triple systems

Abstract

Let D ∗ ( v ) {D^ \ast }(v) denote the maximum number of pairwise disjoint and isomorphic Steiner triple systems of order v. The main result of this paper is a lower bound for D ∗ ( v ) {D^\ast }(v) , namely D ∗ ( 6 t + 3 ) ≧ 4 t − 1 {D^\ast }(6t + 3) \geqq 4t - 1 or 4 t + 1 4t + 1 according as 2 t + 1 2t + 1 is or is not divisible by 3, and D ∗ ( 6 t + 1 ) ≧ t / 2 {D^ \ast }(6t + 1) \geqq t/2 or t according as t is even or odd. Some other related problems are studied or proposed for study.