Let m_2(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 q^2 - q + 5 for m'_2(3, q), q even and q \geq 8, will be improved. As a corollary new bounds for m_2(n, q), q even, q\geq 8 and n \geq 4, are obtained. Cao and Ou published a better bound but there seems to be a gap in their proof.
@article{arxiv.1702.01097,
title = {On k-caps in PG(n, q), with q even and n \geq 3},
author = {J. A. Thas},
journal= {arXiv preprint arXiv:1702.01097},
year = {2017}
}