On k-caps in PG(n, q), with q even and n ≥ 3
Abstract
Let m2(n, q) be the maximum size of k for which there exists a k-cap in PG(n, q), and let m'2(n, q) be the second largest value of k for which there exists a complete k-cap in PG(n, q). In this paper Chao's upper bound q2 - q + 5 for m'2(3, q), q even and q ≥ 8, will be improved. As a corollary new bounds for m2(n, q), q even, q≥ 8 and n ≥ 4, are obtained. Cao and Ou published a better bound but there seems to be a gap in their proof.
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