---
res:
bibo_abstract:
- "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.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Charlene
foaf_name: Weiß, Charlene
foaf_surname: Weiß
foaf_workInfoHomepage: http://www.librecat.org/personId=70420
dct_date: 2023^xs_gYear
dct_language: eng
dct_title: Nontrivial $t$-designs in polar spaces exist for all $t$@
...