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Large sets of disjoint group-divisible designs with block size three and type 2 n 4 1 (denoted by L S ( 2 n 4 1 ) ) were first studied by Schellenberg and Stinson and motivated by their connection with perfect threshold schemes. It has been shown that the necessary condition n ≡ 0 ( m o d 3 ) for the existence of an L S ( 2 n 4 1 ) is sufficient with five possible exceptions n ∈ { 12 , 30 , 36 , 48 , 144 } . These five undetermined L S ( 2 n 4 1 ) s are shown to exist in this paper. [ABSTRACT FROM AUTHOR]

Abstract: Franek et al. recently described four constructions for large sets of -intersecting Steiner triple systems of order (STS ) [F. Franek, M.J. Grannell, T.S. Griggs, A. Rosa, On the large sets of -intersecting Steiner triple systems of order , Des. Codes Cryptogr. 26 (2002) 243–256]. In this study we focus on large sets of -intersecting STS . 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 -intersecting KTS are used to produce some new large sets of Kirkman triple systems. [Copyright &y& Elsevier]