Constructions of nested directed BIB designs

A directed BIB design DB(k, A; v) is a BIB design B(k, 2A; v) in which the blocks are transitively ordered k-tuples and each ordered pair of elements occurs in exactly A blocks. A nested directed BIB design NDB(k, A; v) of form IT2<n<k-l(njn, An)in is a DB(k, A; v) where each block contains E2<n<k-l injn mutually disjoint subblocks, injn subblocks of which are partitIoned into in mutually disjoint families of jn subblocks of size nand the jn subblocks of size n belong to one distinguished system which forms the collection of blocks of a DB(n, An; v). In this paper we will use known and new techniques to show the existence of all NDB(k, A; v) of the form IT2SnSk-l (n jn , An)in for k = 4 and 5. Australasian Journal of Combinatorics 18(1998), pp.157-172