---
_id: '50299'
abstract:
- lang: eng
text: "A finite classical polar space of rank $n$ consists of the totally isotropic\r\nsubspaces
of a finite vector space over $\\mathbb{F}_p$ equipped with a\r\nnondegenerate
form such that $n$ is the maximal dimension of such a subspace. A\r\n$t$-$(n,k,\\lambda)$
design in a finite classical polar space of rank $n$ is a\r\ncollection $Y$ of
totally isotropic $k$-spaces such that each totally isotropic\r\n$t$-space is
contained in exactly $\\lambda$ members of $Y$. Nontrivial examples\r\nare currently
only known for $t\\leq 2$. We show that $t$-$(n,k,\\lambda)$\r\ndesigns in polar
spaces exist for all $t$ and $p$ provided that\r\n$k>\\frac{21}{2}t$ and $n$ is
sufficiently large enough. The proof is based on a\r\nprobabilistic method by
Kuperberg, Lovett, and Peled, and it is thus\r\nnonconstructive."
author:
- first_name: Charlene
full_name: Weiß, Charlene
id: '70420'
last_name: Weiß
citation:
ama: Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. *arXiv:231108288*.
apa: Weiß, C. (n.d.). Nontrivial $t$-designs in polar spaces exist for all $t$.
In *arXiv:2311.08288*.
bibtex: '@article{Weiß, title={Nontrivial $t$-designs in polar spaces exist for
all $t$}, journal={arXiv:2311.08288}, author={Weiß, Charlene} }'
chicago: Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.”
*ArXiv:2311.08288*, n.d.
ieee: C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” *arXiv:2311.08288*.
.
mla: Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.”
*ArXiv:2311.08288*.
short: C. Weiß, ArXiv:2311.08288 (n.d.).
date_created: 2024-01-08T14:39:54Z
date_updated: 2024-01-08T14:41:18Z
department:
- _id: '100'
external_id:
arxiv:
- '2311.08288'
language:
- iso: eng
publication: arXiv:2311.08288
publication_status: submitted
status: public
title: Nontrivial $t$-designs in polar spaces exist for all $t$
type: preprint
user_id: '70420'
year: '2023'
...