On k-caps in PG(n, q), with q even and n \geq 4

TL;DR

This paper improves bounds on the maximum size of complete k-caps in projective spaces PG(n, q) for even q and n ≥ 4, with q ≥ 2048, advancing understanding in finite geometry.

Contribution

It provides significantly improved bounds for the maximum size of complete k-caps in PG(n, q) for large even q and n ≥ 4, extending previous results.

Findings

New upper bounds for m_2(n, q) with q even and q ≥ 2048

Enhanced understanding of complete k-caps in high-dimensional projective spaces

Progress in finite geometry bounds for large finite fields

Abstract

Let $m_2(n, q), n \geq 3$, be the maximum size of k for which there exists a complete k-cap in PG(n, q). In this paper the known bounds for $m_2(n, q), n \geq 4$, q even and $q \geq 2048$, will be considerably improved.