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On the non-existence of a maximal partial spread of size 76 in PG(3,9)

(2008) Ars Combinatoria. 89. p.369-382
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Abstract
We prove the non-existence of maximal partial spreads of size 76 in PG(3,9). Relying on the classification of the minimal blocking sets of size 15 in PG(2, 9) [22], we show that there are only two possibilities for the set of holes of such a maximal partial spread. The weight argument of Blokhuis and Metsch [3] then shows that these sets cannot be the set of holes of a maximal partial spread of size 76. In [17], the non-existence of maximal partial spreads of size 75 in PG(3,9) is proven. This altogether proves that the largest maximal partial spreads, different from a spread, in PG(3, q = 9) have size q(2) - q + 2 = 74.

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Citation

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MLA
Heden, Olof et al. “On the Non-existence of a Maximal Partial Spread of Size 76 in PG(3,9).” Ars Combinatoria 89 (2008): 369–382. Print.
APA
Heden, O., Marcugini, S., Pambianco, F., & Storme, L. (2008). On the non-existence of a maximal partial spread of size 76 in PG(3,9). Ars Combinatoria, 89, 369–382.
Chicago author-date
Heden, Olof, Stefano Marcugini, Fernanda Pambianco, and Leo Storme. 2008. “On the Non-existence of a Maximal Partial Spread of Size 76 in PG(3,9).” Ars Combinatoria 89: 369–382.
Chicago author-date (all authors)
Heden, Olof, Stefano Marcugini, Fernanda Pambianco, and Leo Storme. 2008. “On the Non-existence of a Maximal Partial Spread of Size 76 in PG(3,9).” Ars Combinatoria 89: 369–382.
Vancouver
1.
Heden O, Marcugini S, Pambianco F, Storme L. On the non-existence of a maximal partial spread of size 76 in PG(3,9). Ars Combinatoria. 2008;89:369–82.
IEEE
[1]
O. Heden, S. Marcugini, F. Pambianco, and L. Storme, “On the non-existence of a maximal partial spread of size 76 in PG(3,9),” Ars Combinatoria, vol. 89, pp. 369–382, 2008.
@article{682295,
  abstract     = {We prove the non-existence of maximal partial spreads of size 76 in PG(3,9). Relying on the classification of the minimal blocking sets of size 15 in PG(2, 9) [22], we show that there are only two possibilities for the set of holes of such a maximal partial spread. The weight argument of Blokhuis and Metsch [3] then shows that these sets cannot be the set of holes of a maximal partial spread of size 76. In [17], the non-existence of maximal partial spreads of size 75 in PG(3,9) is proven. This altogether proves that the largest maximal partial spreads, different from a spread, in PG(3, q = 9) have size q(2) - q + 2 = 74.},
  author       = {Heden, Olof and Marcugini, Stefano and Pambianco, Fernanda and Storme, Leo},
  issn         = {0381-7032},
  journal      = {Ars Combinatoria},
  language     = {eng},
  pages        = {369--382},
  title        = {On the non-existence of a maximal partial spread of size 76 in PG(3,9)},
  volume       = {89},
  year         = {2008},
}

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