Designs, Codes and Cryptography

, Volume 54, Issue 2, pp 101–107 | Cite as

The maximum size of a partial 3-spread in a finite vector space over GF(2)

  • S. El-Zanati
  • H. Jordon
  • G. Seelinger
  • P. Sissokho
  • L. Spence


Let n ≥ 3 be an integer, let V n (2) denote the vector space of dimension n over GF(2), and let c be the least residue of n modulo 3. We prove that the maximum number of 3-dimensional subspaces in V n (2) with pairwise intersection {0} is \({\frac{2^n-2^c}{7}-c}\) for n ≥ 8 and c = 2. (The cases c = 0 and c = 1 have already been settled.) We then use our results to construct new optimal orthogonal arrays and (s, k, λ)-nets.


Spreads Partial spreads Orthogonal arrays (s, k, λ)-nets 

Mathematics Subject Classification (2000)

51E23 05B40 05B15 11T71 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • S. El-Zanati
    • 1
  • H. Jordon
    • 1
  • G. Seelinger
    • 1
  • P. Sissokho
    • 1
  • L. Spence
    • 1
  1. 1.4520 Mathematics DepartmentIllinois State UniversityNormalUSA

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