Constructions for large sets of -intersecting Steiner triple systems of order

Franek et al. recently described four constructions for large sets of v − 1 L -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 − 1 L -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 , v 3 } -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 , v 3 } -intersecting KTS ( v ) are used to produce some new large sets of Kirkman triple systems.