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On the non-existence of a maximal partial spread of size 76 in PG(3,9)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Ars combinatoria, ISSN 0381-7032, Vol. 89, 369-382 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2008. Vol. 89, 369-382 p.
Keyword [en]
n-queen problem, nets, sets
Identifiers
URN: urn:nbn:se:kth:diva-17886ISI: 000260018500030Scopus ID: 2-s2.0-56649092567OAI: oai:DiVA.org:kth-17886DiVA: diva2:335931
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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