On (k,n)-blocking sets which can be obtained as a union of conics

A family of conics in PG(2,q) is called saturated if any line LPG(2,q) is incident with at least one conic of the family. Then, if <(q+1)/2, the support of is a (k,n)-blocking set. It is shown that in this way one can get blocking sets whose character n is small compared to q; it is also shown that cannot be taken independent of q, but must necessarily increase as q does.