Enumerations of (K_4-e)-designs with small orders
  It is established that up to isomorphism,there are only one (K_4-e)-design of order 6, three (K_4-e)-designs of order 10 and two (K_4-e)-designs of order 11. As an application of our enumerative results, we discuss the fine triangle intersection problem for (K_4-e)-designs of orders v=6,10,11. 
Yanxun Chang, Tao Feng, Giovanni Lo Faro, and Antoinette Tripodi
math.CO