We classify the minimal blocking sets of size 15 in P G(2, 9). We show that the only examples are the projective triangle and the sporadic ex- ample arising from the secants to the unique complete 6-arc in P G(2, 9). This classification was used to solve the open problem of the existence of maximal partial spreads of size 76 in P G(3, 9). No such maximal par- tial spreads exist [13]. In [14], also the non-existence of maximal partial spreads of size 75 in P G(3, 9) has been proven. So, the result presented here contributes to the proof that the largest maximal partial spreads in P G(3, q = 9) have size q 2 − q + 2 = 74.
Minimal blocking sets in PG(2,9)
PAMBIANCO, Fernanda
2008
Abstract
We classify the minimal blocking sets of size 15 in P G(2, 9). We show that the only examples are the projective triangle and the sporadic ex- ample arising from the secants to the unique complete 6-arc in P G(2, 9). This classification was used to solve the open problem of the existence of maximal partial spreads of size 76 in P G(3, 9). No such maximal par- tial spreads exist [13]. In [14], also the non-existence of maximal partial spreads of size 75 in P G(3, 9) has been proven. So, the result presented here contributes to the proof that the largest maximal partial spreads in P G(3, q = 9) have size q 2 − q + 2 = 74.File in questo prodotto:
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