preprint
Nontrivial $t$-designs in polar spaces exist for all $t$
submitted
Charlene
Weiß
author 70420
100
department
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
eng
arXiv:2311.08288
2311.08288
C. Weiß, ArXiv:2311.08288 (n.d.).
C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” <i>arXiv:2311.08288</i>. .
@article{Weiß, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, journal={arXiv:2311.08288}, author={Weiß, Charlene} }
Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>ArXiv:2311.08288</i>, n.d.
Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” <i>ArXiv:2311.08288</i>.
Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. <i>arXiv:231108288</i>.
Weiß, C. (n.d.). Nontrivial $t$-designs in polar spaces exist for all $t$. In <i>arXiv:2311.08288</i>.
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