Subsets of {P}⁴ with no four points on a plane

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.