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It is known that H(2n,q2), n⩾2, does not have ovoids. We improve this result of Thas by showing that the smallest cardinality of a set of points of H(2n,q2) meeting all generators of H(2n,q2) is q2n-2(q3+1). Up to isomorphism there is only one example of this size, and this consists of the points of a cone Sn-2H(2,q2) that do not lie in the vertex Sn-2 of the cone.
We characterize the smallest minimal blocking sets of Q(2n,q), q an odd prime, in terms of ovoids of Q(4,q) and Q(6,q). The proofs of these results are written for q=3,5,7 since for these values it was known that every ovoid of Q(4,q) is an elliptic quadric. Recently, in Ball et al. (Des. Codes Cryptogr., to appear), it has been proven that for all q prime, every ovoid of Q(4,q) is an elliptic quadric...
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