Subsets of P⁴ with no four points on a plane

Geertrui Van de Voorde; José Felipe Voloch

doi:10.1007/s00013-026-02270-x

July 16, 2026Archiv der MathematikOpen Access

Subsets of P⁴ with no four points on a plane

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Key Points

To construct a maximal subset of ${\mathbb {P}}^4$ with no four collinear points in any finite field of order q where 3 is not a square.
Developed a new construction technique for subset formation in ${\mathbb {P}}^4$ over finite fields.
Analyzed the size of the constructed subsets.
The constructed set contains $2q + 1$ points.
It achieves maximal size concerning inclusion.
This is the largest known subset satisfying the condition.

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Implication

New construction finds a maximal subset in ${\mathbb {P}}^4$, avoiding four collinear points, in finite fields.

Abstract

We describe a new construction of a subset of P⁴ 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 $$2q+1$$ 2 q + 1 , is maximal with respect to inclusion, and is the largest known such set.

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Cite This Study

Voorde et al. (2026) studied this question.

synapsesocial.com/papers/6a5b176318557b26c2039a02 https://doi.org/10.1007/s00013-026-02270-x

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Subsets of P⁴ with no four points on a plane

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

Subsets of P⁴ with no four points on a plane

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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