A completion of LS(2n41)

Large sets of disjoint group-divisible designs with block size three and type 2n41 (denoted by LS(2n41)) 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 (mod3) for the existence of an LS(2n41) is sufficient with five possible exceptions n∈{12,30,36,48,144}. These five undetermined LS(2n41)s are shown to exist in this paper.