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 q 2 + 1 k q 2 + 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 [13] and Sage [9], we find that there exist no T-blocking sets of size q 2 + 1 for each odd prime power q 13.
For a fixed hyperbolic quadric 𝓗 in PG(3, q), let 𝔼 (respectively 𝕋, 𝕊) denote the set of all lines of PG(3, q) which are external (respectively tangent, secant) with respect to 𝓗. We characterize the minimum size blocking sets of PG(3, q) with respect to each of the line sets 𝕊, 𝕋 ∪ 𝕊 and 𝔼 ∪ 𝕊.
Let H be a hyperbolic quadric in P G(3, q), where q is a prime power. Let E (respectively, T) denote the set of all lines of P G(3, q) which are external (respectively, tangent) to H. We characterize the minimum size blocking sets in P G(3, q), q = 2, with respect to the line set E ∪ T. We also give an alternate proof characterizing the minimum size blocking sets in P G(3, q) with respect to the line set E for all odd q.
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