The fine triangle intersection problem for (K4−e)-designs

Let Fin(v)={(s,t):∃ a pair of (K4−e)-designs of order v intersecting in s blocks and 2s+t triangles}. Let Adm(v)={(s,t):s+t≤bv,s∈J(v),2s+t∈JT(v)}∖{(bv−3,1)}, where J(v) (or JT(v)) denotes the set of positive integers s (or t) such that there exists a pair of (K4−e)-designs of order v intersecting in s blocks (or t triangles), and bv=v(v−1)/10. It is established that Fin(v)=Adm(v) for any integer v≡0,1(mod5), v≥6 and v≠10,11.