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On small blocking sets and their linearity

2008
*
Journal of combinatorial theory. Series A
*

We prove that a

doi:10.1016/j.jcta.2008.01.006
fatcat:whgd74xfwndx3kvqx3lwf7ieg4
*small*minimal*blocking**set*of PG(2, q) is "very close" to be a linear*blocking**set*over some subfield GF(p e ) < GF(q). ... This implies that (i) a similar result holds in PG(n, q) for*small*minimal*blocking**sets*with respect to k-dimensional subspaces (0 k n) and (ii) most of the intervals in the interval-theorems of Szőnyi ... In Section 3 the known bounds and structure results*on**small**blocking**sets*are enlisted. ...##
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On the stability of small blocking sets

2013
*
Journal of Algebraic Combinatorics
*

A stability theorem says that a nearly extremal object can be obtained from an extremal

doi:10.1007/s10801-013-0487-0
fatcat:q5ldvbcixvfntj3zpkoewhaf5m
*one*by "*small*changes". In this paper, we study the relation of*sets*having few 0-secants and*blocking**sets*. ... A*blocking**set*is minimal, when no proper subset of it is a*blocking**set*. ... Many of them concentrate*on**small**blocking**sets*of PG (2, q) , these are*blocking**sets*whose cardinality is less than 3 2 (q + 1). ...##
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On Small Sets of Distribution Functions of Ratio Block Sequences

2016
*
Uniform Distribution Theory
*

*One*of the most interesting is that using the

*set*of all distribution functions of the corresponding ratio

*block*sequence introduced in [Strauch, O.—Tóth, J.T.: Publ. Math. ... In the present paper we give some sufficient conditions under which this

*set*is

*small*in a metric sense. As a corollary we obtain a new characterization of the case of asymptotic distribution. ...

*One*of the most challenging open problem of theory of

*sets*of distribution functions of ratio

*block*sequences is that of characterization of all possible

*sets*G(X n ), see [SN] . ...

##
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Characterization results on small blocking sets of the polar spaces Q +(2n + 1, 2) and Q +(2n + 1, 3)

2007
*
Designs, Codes and Cryptography
*

In [8] , De Beule and Storme characterized the smallest

doi:10.1007/s10623-007-9087-0
fatcat:xpevzo3okngzhnc3f7cbhmopbe
*blocking**sets*of the hyperbolic quadrics Q + (2n + 1, 3), n ≥ 4; they proved that these*blocking**sets*are truncated cones over the unique ovoid of ... This means that the two smallest minimal*blocking**sets*of Q + (2n + 1, 2), n ≥ 3, are classified. ... The lines*on*S meeting B form a minimal*blocking**set*in the quotient geometry*on*S (Corollary 2.2). This*blocking**set*is not an ovoid, since the lines SR 1 and SR 2 are perpendicular. ...##
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Manufacturing optimization using Tsukamoto fuzzy inference system method: A case study in block paving and solid concrete block industry

2018
*
MATEC Web of Conferences
*

While the number of

doi:10.1051/matecconf/201820402002
fatcat:gkcpbrdbibeoxcyiuroo4xkuaa
*block*paving produced by the company*on*the period of ... From the calculations, the number of solid concrete*block*produced by the company*on*the period of October 2016, December 2016 and February 2017 was not optimal. ... Kawan Setia is*one*of the manufacturing companies engaged in the manufacture of solid concrete*block*and*block*paving. ...##
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Small-LRU: A Hardware Efficient Hybrid Replacement Policy

2020
*
International Journal of Advanced Computer Science and Applications
*

Modern LLCs are divided into multiple banks where each bank is a

doi:10.14569/ijacsa.2020.0110981
fatcat:dyrh76k575dtbbwzo6xinuz4ia
*set*-associative cache. ... The replacement policy implemented*on*such highly associative banks consume significant hardware (storage and area) overhead. ... To insert a newly incoming*block*in the*set*,*one*of the existing*block*need to be evicted first known as the victim*block*. ...##
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A small minimal blocking set in PG(n, p t ), spanning a (t − 1)-space, is linear

2012
*
Designs, Codes and Cryptography
*

In this paper, we show that a

doi:10.1007/s10623-012-9751-x
fatcat:62xiejltr5a5fnmaapuryllpru
*small*minimal*blocking**set*with exponent e in PG(n, p t ), p prime, spanning a (t/e − 1)-dimensional space, is an F p e -linear*set*, provided that p > 5(t/e) − 11. ... As a corollary, we get that all*small*minimal*blocking**sets*in PG(n, p t ), p prime, p > 5t − 11, spanning a (t − 1)-dimensional space, are F p -linear, hence confirming the linearity conjecture for*blocking*... A*blocking**set*B is called*small*if |B| < 3(q + 1)/2 and minimal if no proper subset of B is a*blocking**set*. ...##
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On the linearity of higher-dimensional blocking sets
[article]

2012
*
arXiv
*
pre-print

A

arXiv:1201.3300v1
fatcat:asrb2yuto5finiapgccwhtq6f4
*small*minimal k-*blocking**set*B in PG(n, q), q = pt, p prime, is a*set*of less than 3(qk + 1)/2 points in PG(n, q), such that every (n - k)-dimensional space contains at least*one*point of B and such ... Furthermore, we show that the linearity of*small*minimal*blocking**sets*in PG(2, q) implies the linearity of*small*minimal k-*blocking**sets*in PG(n, pt), with exponent e, with pe \geq t/e + 11. ... Previous results In this section, we list a few results*on*the linearity of*small*minimal k-*blocking**sets*and*on*the size of*small*k-*blocking**sets*that will be used throughout this paper. ...##
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Constructing minimal blocking sets using field reduction
[article]

2015
*
arXiv
*
pre-print

of the

arXiv:1512.04822v1
fatcat:xqdxixcdebgj3nocrgr2n3gyou
*blocking*cone over a planar*blocking**set*, we obtain larger*blocking**sets*than the*ones*obtained from planar*blocking**sets*in pol. ... We show that if a*small*minimal*blocking**set*is constructed from the MPS-construction, it is of Rédei-type whereas a*small*minimal*blocking**set*arises from our cone construction if and only if it is linear ... This also provides us with a different view*on*the linearity conjecture for*small*minimal*blocking**sets*. ...##
###
Small point sets of PG(n, p 3h ) intersecting each line in 1 mod p h points

2010
*
Journal of Geometry
*

*sets*with respect to lines) are linear

*blocking*

*sets*. ... The main result of this paper is that point

*sets*of PG(n, q), q = p 3h , p ≥ 7 prime, of size less than 3(q n−1 + 1)/2 intersecting each line in 1 modulo 3 √ q points (these are always

*small*minimal

*blocking*...

*Small*minimal

*blocking*

*sets*There has been a lot of attention paid

*on*

*small*minimal (planar)

*blocking*

*sets*. Bruen showed that a non-trivial

*blocking*

*set*has size at least q + √ q + 1. ...

##
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Constructing Minimal Blocking Sets Using Field Reduction

2015
*
Journal of combinatorial designs (Print)
*

of the

doi:10.1002/jcd.21432
fatcat:yxolr5pllzdvvm5a45vt2q7ble
*blocking*cone over a planar*blocking**set*, we obtain larger*blocking**sets*than the*ones*obtained from planar*blocking**sets*in [15] . ... We show that if a*small*minimal*blocking**set*is constructed from the MPSconstruction, it is of Rédei-type whereas a*small*minimal*blocking**set*arises from our cone construction if and only if it is linear ... This also provides us with a different view*on*the linearity conjecture for*small*minimal*blocking**sets*. ...##
###
Page 920 of Automation and Remote Control Vol. 37, Issue 6
[page]

1976
*
Automation and Remote Control
*

This distance depends, first,

*on*how the subset of vertices of the initial graph (*block*) correspond to the vertices of the*small*graph, and, second, what kind of structure the*small*graph possesses, To ... Muchnik UDC 519.283 Approximation of a graph by*one*with a*small*number of vertices, posed in [4], is considered. ...##
###
Page 954 of Journal of Cognitive Neuroscience Vol. 12, Issue 6
[page]

2000
*
Journal of Cognitive Neuroscience
*

*set*of large

*blocks*in the subsequent

*set*of test trials was subtracted from the response to the

*block*that would be matched to the

*set*of

*small*

*blocks*. ... As expected, in the initial baseline trials, the difference calculated between estimates of the probe

*blocks*based

*on*whether they were to be matched to the

*set*of large or

*small*key

*blocks*was not significant ...

##
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Page 610 of IEEE Transactions on Computers Vol. 52, Issue 5
[page]

2003
*
IEEE Transactions on Computers
*

When particular

*small**block*is accessed by the CPU, th corresponding hit bit is*set*to*one*. Thus, the hit bit: the*small**block*identifies it as a referenced*block*2. ... The data in the*small**block*are sent to the CPU and the hit bit is*set*to mark it as referenced. ...##
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Page 159 of American Society of Civil Engineers. Collected Journals Vol. 3, Issue AE4
[page]

1997
*
American Society of Civil Engineers. Collected Journals
*

15 Epoxy” (

*one*week*set*), no toe nails 15 Epoxy* (*one*week*set*), toe-nailed when epoxy was wet 16 Toe nail + epoxy*on**small*wood*blocks*’ (*one*week*set*) Toe nail + epoxy*on**small*wood*blocks*(24—48 hr. ...*set*) Toe nail + epoxy*on*large wood*blocks** (*one*week*set*) Acrylic adhesive” (*one*week*set*), toe-nailed when adhesive was wet Acrylic adhesive” (*one*week*set*), wood first soaked 24 h, toe-nailed when ...
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