Minimum size blocking sets of certain line sets related to a conic in PG(2,q)PG(2,q)

Let EE (respectively; TT, SS) denote the set of all lines which are external (respectively; tangent, secant) to an irreducible conic in PG(2,q)PG(2,q). We give a brief survey of the known results regarding the minimum size LL-blocking sets of PG(2,q)PG(2,q) for L∈{E,S,T∪E,T∪S}L∈{E,S,T∪E,T∪S} and study the other two cases when L=TL=T, E∪SE∪S.