Nontrivial $t$-designs in polar spaces exist for all $t$
Weiß, Charlene
A finite classical polar space of rank $n$ consists of the totally isotropic
subspaces of a finite vector space over $\mathbb{F}_p$ equipped with a
nondegenerate form such that $n$ is the maximal dimension of such a subspace. A
$t$-$(n,k,\lambda)$ design in a finite classical polar space of rank $n$ is a
collection $Y$ of totally isotropic $k$-spaces such that each totally isotropic
$t$-space is contained in exactly $\lambda$ members of $Y$. Nontrivial examples
are currently only known for $t\leq 2$. We show that $t$-$(n,k,\lambda)$
designs in polar spaces exist for all $t$ and $p$ provided that
$k>\frac{21}{2}t$ and $n$ is sufficiently large enough. The proof is based on a
probabilistic method by Kuperberg, Lovett, and Peled, and it is thus
nonconstructive.
2023
info:eu-repo/semantics/preprint
doc-type:preprint
text
http://purl.org/coar/resource_type/c_816b
https://ris.uni-paderborn.de/record/50299
Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. <i>arXiv:231108288</i>.
eng
info:eu-repo/semantics/altIdentifier/arxiv/2311.08288
info:eu-repo/semantics/closedAccess