{"page":"971 - 981","_id":"50299","volume":93,"date_updated":"2026-02-25T13:51:50Z","publication":"Des. Codes Cryptogr.","date_created":"2024-01-08T14:39:54Z","year":"2025","type":"journal_article","language":[{"iso":"eng"}],"status":"public","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>","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>.","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} }","short":"C. Weiß, Des. Codes Cryptogr. 93 (2025) 971–981."},"user_id":"70420","publication_status":"published","department":[{"_id":"100"}],"title":"Nontrivial $t$-designs in polar spaces exist for all $t$","author":[{"last_name":"Weiß","id":"70420","first_name":"Charlene","full_name":"Weiß, Charlene"}],"doi":"10.1007/s10623-024-01471-1","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."}],"intvolume":"        93"}