[{"author":[{"id":"70420","last_name":"Weiß","first_name":"Charlene"}],"dini_type":"doc-type:preprint","external_id":{"arxiv":[]},"publication":"arXiv:2311.08288","type":"preprint","user_id":"70420","date_created":"2024-01-08T14:39:54Z","citation":{"short":"C. Weiß, ArXiv:2311.08288 (n.d.).","ieee":"C. Weiß, “Nontrivial $t$-designs in polar spaces exist for all $t$,” *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.","mla":"Weiß, Charlene. “Nontrivial $t$-Designs in Polar Spaces Exist for All $t$.” *ArXiv:2311.08288*.","apa":"Weiß, C. (n.d.). Nontrivial $t$-designs in polar spaces exist for all $t$. In *arXiv:2311.08288*."},"status":"public","abstract":[{"lang":"eng"}],"uri_base":"https://ris.uni-paderborn.de","dc":{"rights":["info:eu-repo/semantics/closedAccess"],"source":["Weiß C. Nontrivial $t$-designs in polar spaces exist for all $t$. *arXiv:231108288*."],"identifier":["https://ris.uni-paderborn.de/record/50299"],"relation":["info:eu-repo/semantics/altIdentifier/arxiv/2311.08288"],"description":["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."],"date":["2023"],"type":["info:eu-repo/semantics/preprint","doc-type:preprint","text","http://purl.org/coar/resource_type/c_816b"],"creator":["Weiß, Charlene"],"language":["eng"],"title":["Nontrivial $t$-designs in polar spaces exist for all $t$"]},"publication_status":"submitted","date_updated":"2024-01-08T14:41:18Z","creator":{"login":"chweiss","id":"70420"},"language":[{}],"_id":"50299","department":[{"_id":"100","tree":[{"_id":"99"},{"_id":"10"},{"_id":"34"},{"_id":"44"},{"_id":"43"}]}]}]