[{"citation":{"chicago":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” *ArXiv:2311.08288*, n.d.","bibtex":"@article{Weiß, title={Nontrivial $t$-designs in polar spaces exist for all $t$}, journal={arXiv:2311.08288}, author={Weiß, Charlene} }","ieee":"C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” *arXiv:2311.08288*. .","short":"C. Weiß, ArXiv:2311.08288 (n.d.).","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*.","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” *ArXiv:2311.08288*."},"status":"public","date_created":"2024-01-08T14:39:54Z","user_id":"70420","type":"preprint","publication":"arXiv:2311.08288","external_id":{"arxiv":["2311.08288"]},"author":[{"id":"70420","full_name":"Weiß, Charlene","last_name":"Weiß","first_name":"Charlene"}],"department":[{"_id":"100"}],"_id":"50299","title":"Nontrivial $t$-designs in polar spaces exist for all $t$","language":[{"iso":"eng"}],"year":"2023","publication_status":"submitted","date_updated":"2024-01-08T14:41:18Z","abstract":[{"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.","lang":"eng"}]}]