A completion of [formula omitted].

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]