---
_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 $\\mathbb{F}_q$ 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 $q$ 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 $t$. <i>Des Codes
    Cryptogr</i>. 2025;93:971-981. doi:<a href="https://doi.org/10.1007/s10623-024-01471-1">10.1007/s10623-024-01471-1</a>
  apa: Weiß, C. (2025). Nontrivial $t$-designs in polar spaces exist for all $t$.
    <i>Des. Codes Cryptogr.</i>, <i>93</i>, 971–981. <a href="https://doi.org/10.1007/s10623-024-01471-1">https://doi.org/10.1007/s10623-024-01471-1</a>
  bibtex: '@article{Weiß_2025, title={Nontrivial $t$-designs in polar spaces exist
    for all $t$}, volume={93}, DOI={<a href="https://doi.org/10.1007/s10623-024-01471-1">10.1007/s10623-024-01471-1</a>},
    journal={Des. Codes Cryptogr.}, author={Weiß, Charlene}, year={2025}, pages={971–981}
    }'
  chicago: 'Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All
    $t$.” <i>Des. Codes Cryptogr.</i> 93 (2025): 971–81. <a href="https://doi.org/10.1007/s10623-024-01471-1">https://doi.org/10.1007/s10623-024-01471-1</a>.'
  ieee: 'C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” <i>Des.
    Codes Cryptogr.</i>, vol. 93, pp. 971–981, 2025, doi: <a href="https://doi.org/10.1007/s10623-024-01471-1">10.1007/s10623-024-01471-1</a>.'
  mla: Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.”
    <i>Des. Codes Cryptogr.</i>, vol. 93, 2025, pp. 971–81, doi:<a href="https://doi.org/10.1007/s10623-024-01471-1">10.1007/s10623-024-01471-1</a>.
  short: C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981.
date_created: 2024-01-08T14:39:54Z
date_updated: 2026-02-25T13:51:50Z
department:
- _id: '100'
doi: 10.1007/s10623-024-01471-1
intvolume: '        93'
language:
- iso: eng
page: 971 - 981
publication: Des. Codes Cryptogr.
publication_status: published
status: public
title: Nontrivial $t$-designs in polar spaces exist for all $t$
type: journal_article
user_id: '70420'
volume: 93
year: '2025'
...