Extended Have Large Sets Of Directed Triple Systems Construction

Large set of pairwise disjoint Mendelsohn triple systems (LMTS) and large set of pairwise disjoint transitive triple systems (LDTS) are two kinds of large set of oriented designs. The existence of LMTS and LDTS has been proved. The two kinds of large set above-mentioned are called large set of pairwise disjoint extended Mendelsohn triple systems (LEMTS(v)) and large set of pairwise disjoint extended transitive triple systems (LEDTS(v)) respectively if oriented pair (z, x) occurs in them. It is well known that an LEMTS(v) contains v EMTS(v)s and an LEDTS(v) contains 3v - 2 EDTS(v)s. In this paper, the spectrum of LEDTS(v) is proved. Meanwhile, for LEDTS(v), a three triple recursive construction is given.