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), 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 then shows that these sets cannot be the set of holes of a maximal partial spread of size 76. Previously we have proven the non-existence of maximal partial spreads of size 75 in PG(3,9). 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.
Non existence of a maximal partial spread of size 76 in PG(3,9)
MARCUGINI, Stefano;PAMBIANCO, Fernanda;
2008
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), 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 then shows that these sets cannot be the set of holes of a maximal partial spread of size 76. Previously we have proven the non-existence of maximal partial spreads of size 75 in PG(3,9). 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
