complete caps
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2018 ◽  
Vol 18 (5) ◽  
pp. 54-62
Author(s):  
Alexander A. Davydov ◽  
Stefano Marcugini ◽  
Fernanda Pambianco

Abstract We propose the concepts of almost complete subset of an elliptic quadric in the projective space PG(3, q) and of almost complete cap in the space PG(N, q), N ≥ 3, as generalizations of the concepts of almost complete subset of a conic and of almost complete arc in PG(2, q). Upper bounds of the smallest size of the introduced geometrical objects are obtained by probabilistic and algorithmic methods.



2017 ◽  
Vol 25 (9) ◽  
pp. 419-425 ◽  
Author(s):  
Daniele Bartoli ◽  
Giorgio Faina ◽  
Stefano Marcugini ◽  
Fernanda Pambianco
Keyword(s):  


COMBINATORICA ◽  
2017 ◽  
Vol 38 (2) ◽  
pp. 255-278 ◽  
Author(s):  
Daniele Bartoli ◽  
Massimo Giulietti ◽  
Giuseppe Marino ◽  
Olga Polverino
Keyword(s):  


2016 ◽  
Vol 108 (1) ◽  
pp. 215-246 ◽  
Author(s):  
Daniele Bartoli ◽  
Giorgio Faina ◽  
Stefano Marcugini ◽  
Fernanda Pambianco


2014 ◽  
Vol 13 (08) ◽  
pp. 1450050 ◽  
Author(s):  
Irene Platoni

In a three-dimensional Galois space of odd order q, the known infinite families of complete caps have size far from the theoretical lower bounds. In this paper, we investigate some caps defined from elliptic curves. In particular, we show that for each q between 100 and 350 they can be extended to complete caps, which turn out to be the smallest complete caps known in the literature.



2014 ◽  
Vol 41 (1) ◽  
pp. 185-216 ◽  
Author(s):  
Nurdagül Anbar ◽  
Daniele Bartoli ◽  
Irene Platoni ◽  
Massimo Giulietti
Keyword(s):  


2013 ◽  
Vol 24 ◽  
pp. 184-191 ◽  
Author(s):  
Daniele Bartoli ◽  
Giorgio Faina ◽  
Massimo Giulietti


2013 ◽  
Vol 22 (10) ◽  
pp. 409-424 ◽  
Author(s):  
Nurdagül Anbar ◽  
Daniele Bartoli ◽  
Massimo Giulietti ◽  
Irene Platoni
Keyword(s):  


2012 ◽  
Vol 38 (2) ◽  
pp. 371-392 ◽  
Author(s):  
Nurdagül Anbar ◽  
Massimo Giulietti


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