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In this paper, ik-blocking sets in iPG(in, iq), being of Rédei type, are investigated. A standard method to construct Rédei type ik-blocking sets in iPG(in, iq) is to construct a cone having as base a Rédei type ik′-blocking set in a subspace of iPG(in, iq). But also other Rédei type ik-blocking sets in iPG(in, iq), which are not cones, exist. We give in this article a condition on the parameters of a Rédei type ik-blocking set of iPG(in, iq = ipih), ip a prime power, which guarantees that the Rédei type ik-blocking set is a cone. This condition is sharp. We also show that small Rédei type ik-blocking sets are linear.

Linear Point Sets and Rédei Type k-blocking Sets in PG(n, q)