Blocking sets of tangent lines to a hyperbolic quadric in PG(3, 3)

Let Q+(3,q) be a hyperbolic quadric in PG(3,q) and T be the set of all lines of PG(3,q) which are tangent to Q+(3,q). If k is the minimum size of a T-blocking set in PG(3,q), then we prove that q2+1≤k≤q2+q. When q=3, we show that: (i) there is no T-blocking set of size 10, and (ii) there are exactly two T-blocking sets of size 11 up to isomorphism. By means of the computer algebra systems GAP (The GAP Group, 2014) and Sage (Sage Mathematics Software (Version 6.3), 2014), we find that there exist no T-blocking sets of size q2+1 for each odd prime power q≤13.