Minimal blocking sets in PG(2, 9)

We classify the minimal blocking sets of size 15 in PG(2, 9). We show that the only examples are the projective triangle and the sporadic example arising from the secants to the unique complete 6-arc in PG(2, 9). This classification was used to solve the open problem of the existence of maximal partial spreads of size 76 in PG(3, 9). No such maximal partial spreads exist [13]. In [14], also the non-existence of maximal partial spreads of size 75 in PG(3, 9) has been proven. So, the result presented here contributes to the proof that the largest maximal partial spreads in PG(3, q = 9) have size q2 - q + 2 = 74.

• Type: Journal
• Year: 2008
• Where: ARSCOM
• Authors: Fernanda Pambianco, Leo Storme
• Keywords: ARSCOM 2008, Maximal Partial Spreads, Minimal Blocking Sets, Projective Triangle