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arXiv · 2408.14714

On $3$-designs from $PGL(2,q)$

Paul Tricot
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Abstract

The group $PGL(2,q)$ acts $3$-transitively on the projective line $GF(q) \cup \{\infty\}$. Thus, an orbit of its action on the $k$-subsets of the projective line is the block set of a $3$-$(q+1,k,λ)$ design. We find the parameters of the designs formed by the orbit of a block of the form $\langle θ^r \rangle$ or $\langle θ^r \rangle \cup \{ 0\}$, where $θ$ is a primitive element of $GF(q)$.

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Paul Tricot. 2024-08-27. On $3$-designs from $PGL(2,q)$. https://arxiv.org/abs/2408.14714

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