Constructions for large sets of v−1  {0,v3}-intersecting Steiner triple systems of order v

Franek et al. recently described four constructions for large sets of v−1L-intersecting Steiner triple systems of order v  (STS(v)) [F. Franek, M.J. Grannell, T.S. Griggs, A. Rosa, On the large sets of v−1L-intersecting Steiner triple systems of order v, Des. Codes Cryptogr. 26 (2002) 243-256]. In this study we focus on large sets of v−1   {0,v3}-intersecting STS(v). Some recursive constructions are presented that involve three-wise balanced designs. By applying these constructions we obtain some new infinite classes of such large sets, and the large sets of v−1{0,v3}-intersecting KTS(v) are used to produce some new large sets of Kirkman triple systems.