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Small Minimal Blocking Sets inPG(2, q3)

✍ Scribed by O Polverino; L Storme


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
109 KB
Volume
23
Category
Article
ISSN
0195-6698

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✦ Synopsis


on small minimal blocking sets in P G(2, p 3 ), p prime, p β‰₯ 7, to small minimal blocking sets in P G(2, q 3 ), q = p h , p prime, p β‰₯ 7, with exponent e β‰₯ h. We characterize these blocking sets completely as being blocking sets of RΓ©dei-type.


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✍ TamΓ‘s SzΕ‘nyi; Antonello Cossidente; AndrΓ‘s GΓ‘cs; Csaba MengyΓ‘n; Alessandro Sicil πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 172 KB πŸ‘ 1 views

## Abstract The size of large minimal blocking sets is bounded by the Bruen–Thas upper bound. The bound is sharp when __q__ is a square. Here the bound is improved if __q__ is a non‐square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non‐p

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We obtain lower bounds for the size of a double blocking set in the Desarguesian projective plane PG(2, q). These bounds are best possible for q Ο½ 11 and in the case q is a square. With the same technique we also exclude certain values for the size of an ordinary minimal blocking set.

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## Abstract We characterize the smallest minimal blocking sets of Q(6,__q__), __q__ even and __q__ β‰₯ 32. We obtain this result using projection arguments which translate the problem into problems concerning blocking sets of Q(4,__q__). Then using results on the size of the smallest minimal blocking

Largest minimal blocking sets in PG(2,8)
✍ J. BarΓ‘t; S. Innamorati πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 120 KB πŸ‘ 1 views

## Abstract Bruen and Thas proved that the size of a large minimal blocking set is bounded by $q \cdot {\sqrt{q}} + 1$. Hence, if __q__ = 8, then the maximal possible size is 23. Since 8 is not a square, it was conjectured that a minimal blocking 23‐set does not exist in PG(2,8). We show that this