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arXiv · 2611.08047

On Grassmann $4$-designs

Mohammad Samy Baladram·Ryutaro Misawa·Akihiro Munemasa
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Abstract

We prove that there is a unique tight $4$-design in the real Grassmannian $G_{2,4}$, up to the action of $O(4)$. Using symmetric association schemes, we also construct an $N$-point $4$-design in $G_{2,4}$ for every even integer $N\geq10$. For symmetric association schemes of order less than $21$, we classify the pairs of rank-three primitive idempotents defining injective maps into $G_{2,4}$; their images are Grassmannian $4$-designs precisely for four schemes of order $16$.

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Mohammad Samy Baladram, Ryutaro Misawa, Akihiro Munemasa. 2026-11-05. On Grassmann $4$-designs. https://arxiv.org/abs/2611.08047

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