We construct an infinite family of transitive $42$-arcs in $\mathrm{PG}(3,q^{2})$, with $q=p^{n}\geq 29$ and $q\equiv 1\pmod{7}$, under the action of the group $\mathrm{PSL}(2,7)$ in its representation as a subgroup of $\mathrm{PGL}(4,q)$. Further, we study the case $q=29$ in detail with computer assistance. For $q=29$ these $42$-arcs turn out to be complete.
Transitive $\mathrm{PSL}(2,7)$-invariant $42$-arcs in $3$-dimensional projective spaces
SONNINO, Angelo
2014-01-01
Abstract
We construct an infinite family of transitive $42$-arcs in $\mathrm{PG}(3,q^{2})$, with $q=p^{n}\geq 29$ and $q\equiv 1\pmod{7}$, under the action of the group $\mathrm{PSL}(2,7)$ in its representation as a subgroup of $\mathrm{PGL}(4,q)$. Further, we study the case $q=29$ in detail with computer assistance. For $q=29$ these $42$-arcs turn out to be complete.File in questo prodotto:
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