Abstract
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.
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Communicated by Dieter Jungnickel.
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El-Zanati, S., Jordon, H., Seelinger, G. et al. The maximum size of a partial 3-spread in a finite vector space over GF(2). Des. Codes Cryptogr. 54, 101–107 (2010). https://doi.org/10.1007/s10623-009-9311-1
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DOI: https://doi.org/10.1007/s10623-009-9311-1