Bruen constructed in 1971 maximal partial spreads in PG(3,q) of the sizes q^2-q+2 and q^2-q+1 when q is odd and a power of a prime. He and Thas conjectured a few years later that the maximum size of a non trivial maximal partial spread in PG(3,q) is q^2-q+2. Recently we, together with Storme, proved that there is no maximal partial spread of size n, for any integer n, in the interval 76<= n<=81. By using the results of a computer search for minimal blocking sets in PG(2,9), we can now prove that there is no maximal partial spread of size 75 in PG(3,9). Thus our results verify the conjecture of Bruen and Thas, in the case q=9. .
The maximal size of a maximal partial spread in PG(3,9)
FAINA, Giorgio;MARCUGINI, Stefano;PAMBIANCO, Fernanda
2010
Abstract
Bruen constructed in 1971 maximal partial spreads in PG(3,q) of the sizes q^2-q+2 and q^2-q+1 when q is odd and a power of a prime. He and Thas conjectured a few years later that the maximum size of a non trivial maximal partial spread in PG(3,q) is q^2-q+2. Recently we, together with Storme, proved that there is no maximal partial spread of size n, for any integer n, in the interval 76<= n<=81. By using the results of a computer search for minimal blocking sets in PG(2,9), we can now prove that there is no maximal partial spread of size 75 in PG(3,9). Thus our results verify the conjecture of Bruen and Thas, in the case q=9. .File in questo prodotto:
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