---
res:
  bibo_abstract:
  - "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@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Ishay
      foaf_name: Haviv, Ishay
      foaf_surname: Haviv
  - foaf_Person:
      foaf_givenName: Sam
      foaf_name: Mattheus, Sam
      foaf_surname: Mattheus
  - foaf_Person:
      foaf_givenName: Aleksa
      foaf_name: Milojević, Aleksa
      foaf_surname: Milojević
  - foaf_Person:
      foaf_givenName: Yuval
      foaf_name: Wigderson, Yuval
      foaf_surname: Wigderson
      foaf_workInfoHomepage: http://www.librecat.org/personId=2d0023a0-1567-11f0-833d-d5c1e476d4b5
  bibo_doi: 10.1016/j.disc.2024.114373
  bibo_issue: '4'
  bibo_volume: 348
  dct_date: 2025^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0012-365X
  dct_language: eng
  dct_publisher: Elsevier@
  dct_subject:
  - Nearly orthogonal sets
  - Ramsey theory
  - Finite fields
  dct_title: Larger nearly orthogonal sets over finite fields@
...