{"date_created":"2026-06-29T10:53:05Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Nearly orthogonal sets","Ramsey theory","Finite fields"],"date_published":"2025-04-01T00:00:00Z","status":"public","issue":"4","year":"2025","publisher":"Elsevier","type":"journal_article","article_type":"original","doi":"10.1016/j.disc.2024.114373","oa_version":"Preprint","_id":"22163","article_number":"114373","das_tickbox":"1","external_id":{"arxiv":["2404.01057"]},"extern":"1","date_updated":"2026-07-14T08:17:17Z","oa":1,"arxiv":1,"language":[{"iso":"eng"}],"author":[{"first_name":"Ishay","last_name":"Haviv","full_name":"Haviv, Ishay"},{"last_name":"Mattheus","first_name":"Sam","full_name":"Mattheus, Sam"},{"first_name":"Aleksa","last_name":"Milojević","full_name":"Milojević, Aleksa"},{"first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","full_name":"Wigderson, Yuval"}],"citation":{"short":"I. Haviv, S. Mattheus, A. Milojević, Y. Wigderson, Discrete Mathematics 348 (2025).","ama":"Haviv I, Mattheus S, Milojević A, Wigderson Y. Larger nearly orthogonal sets over finite fields. <i>Discrete Mathematics</i>. 2025;348(4). doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114373\">10.1016/j.disc.2024.114373</a>","apa":"Haviv, I., Mattheus, S., Milojević, A., &#38; Wigderson, Y. (2025). Larger nearly orthogonal sets over finite fields. <i>Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.disc.2024.114373\">https://doi.org/10.1016/j.disc.2024.114373</a>","chicago":"Haviv, Ishay, Sam Mattheus, Aleksa Milojević, and Yuval Wigderson. “Larger Nearly Orthogonal Sets over Finite Fields.” <i>Discrete Mathematics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.disc.2024.114373\">https://doi.org/10.1016/j.disc.2024.114373</a>.","ista":"Haviv I, Mattheus S, Milojević A, Wigderson Y. 2025. Larger nearly orthogonal sets over finite fields. Discrete Mathematics. 348(4), 114373.","ieee":"I. Haviv, S. Mattheus, A. Milojević, and Y. Wigderson, “Larger nearly orthogonal sets over finite fields,” <i>Discrete Mathematics</i>, vol. 348, no. 4. Elsevier, 2025.","mla":"Haviv, Ishay, et al. “Larger Nearly Orthogonal Sets over Finite Fields.” <i>Discrete Mathematics</i>, vol. 348, no. 4, 114373, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.disc.2024.114373\">10.1016/j.disc.2024.114373</a>."},"article_processing_charge":"No","scopus_import":"1","month":"04","volume":348,"publication_identifier":{"issn":["0012-365X"]},"OA_type":"green","intvolume":"       348","abstract":[{"lang":"eng","text":"For a field F and integers d and k, a set A ⊆ Fd is called k-nearly orthogonal if its\r\nmembers are non-self-orthogonal and every k + 1 vectors of A include an orthogonal pair.\r\nWe prove that for every prime p there exists some δ = δ(p)> 0, such that for every field\r\nF of characteristic p and for all integers k ≥ 2 and d ≥ k, there exists a k-nearly orthogonal\r\nset of at least dδ·k/ logk vectors of Fd. The size of the set is optimal up to the logk term\r\nin the exponent. We further prove two extensions of this result. In the first, we provide a\r\nlarge set A of non-self-orthogonal vectors of Fd such that for every two subsets of A of\r\nsize k+1 each, some vector of one of the subsets is orthogonal to some vector of the other.\r\nIn the second extension, every k + 1 vectors of the produced set A include ℓ + 1 pairwise\r\northogonal vectors for an arbitrary fixed integer 1 ≤ ℓ ≤ k. The proofs involve probabilistic\r\nand spectral arguments and the hypergraph container method"}],"publication":"Discrete Mathematics","OA_place":"repository","publication_status":"published","title":"Larger nearly orthogonal sets over finite fields","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2404.01057 ","open_access":"1"}],"day":"01","quality_controlled":"1"}