Large sets of extended directed triple systems with even orders

AbstractFor three types of triples: unordered, cyclic and transitive, the corresponding extended triple, extended triple system and their large sets are introduced. The existence of LESTS(υ) and LEMTS(υ) were completely solved. In this paper, we shall discuss the existence problem of LEDTS(υ) and give the following conclusion: there exists an LEDTS(υ) for any even υ except υ=4. The existence of LEDTS(υ) with odd order υ will be discussed in another paper, we are working at it