Subsets of P^4 with no four points on a plane

TL;DR

The paper introduces a new construction of large subsets in projective 4-space over certain finite fields that avoid four points lying on a plane, achieving maximal size and advancing understanding of geometric configurations.

Contribution

It presents a novel construction of maximal subsets in P^4 over finite fields where 3 is not a square, expanding known bounds for such geometric configurations.

Findings

Constructs subsets of size 2q + 1 in P^4 with no four points on a plane

Sets are maximal with respect to inclusion in their class

Largest known such sets over the specified finite fields

Abstract

We describe a new construction of a subset of P^4 with no four points on a plane over any finite field of order q in which 3 is not a square. This set has size 2q + 1, is maximal with respect to inclusion, and is the largest known such set.