Constructions of large sets of disjoint group-divisible designs LS(2n41) using a generalization of *LS(2n)

Large sets of disjoint group-divisible designs with block size three and type 2n412n41 were first studied by Schellenberg and Stinson and motivated by their connection with perfect threshold schemes. It is known that such large sets can exist only for n≡0(mod3) and do exist for n=2k(3m)n=2k(3m), where m≡1(mod2) and k=0,3k=0,3 or k≥5k≥5. A special large set called *LS(2n) has played a key role in obtaining the above results. In this paper, we shall give a generalization of an *LS(2n) and use it to obtain a similar result for k=2,4k=2,4 and partially for k=1k=1.