3 citations · 26 across the 14 of their papers we have counts for
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Upper bounds on the smallest size of a complete cap in , , under a certain probabilistic conjecture
Alexander A. Davydov, Giorgio Faina, Stefano Marcugini +1
In the projective space over the Galois field of order , , an iterative step-by-step construction of complete caps by adding a new point on every step…
2-semiarcs in ,
Daniele Bartoli, Giorgio Faina, György Kiss +2
A -semiarc is a pointset with the property that the number of tangent lines to at each of its points is two. Using some theoretical results and…
Tables of sizes of random complete arcs in the plane
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina +2
Tables of sizes of random complete arcs in the plane are given. The sizes are close to the smallest known sizes of complete arcs in , in particular, to ones cons…
Tables, bounds and graphics of sizes of complete arcs in the plane for all and sporadic in obtained by an algorithm with fixed order of points (FOP)
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina +3
In the previous works of the authors, a step-by-step algorithm FOP which uses any fixed order of points in the projective plane is proposed to construct small co…
Tables of parameters of symmetric configurations
Alexander A. Davydov, Giorgio Faina, Massimo Giulietti +2
Tables of the currently known parameters of symmetric configurations are given. Formulas for parameters of the known infinite families of symmetric configurations are presented as…
Tables, bounds and graphics of the smallest known sizes of complete arcs in the plane for all and sporadic in the interval
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina +3
In the projective planes , we collect the smallest known sizes of complete arcs for the regions \begin{align*} &\mbox{all } q\le160001,~~ q \mbox{ prime power};\\…
The nonexistence of an additive quaternary [15,5,9]-code
Daniele Bartoli, Juergen Bierbrauer, Giorgio Faina +2
We show that no additive [15,5,9]_4-code exists. As a consequence the largest dimension k such that an additive quaternary [15,k,9]_4-code exists is k=4.5.
On constructions and parameters of symmetric configurations v_{k}
Alexander A. Davydov, Giorgio Faina, Massimo Giulietti +2
The spectrum of possible parameters of symmetric configurations is investigated. We both survey known constructions and results, and propose some new construction methods. Many new…
Upper bounds on the smallest size of a complete arc in the plane PG(2,q)
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina +2
New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for q <= 9109. From these new bounds it follows that for q <= 2621 a…
On sizes of complete arcs in PG(2,q)
Daniele Bartoli, Alexander A. Davydov, Giorgio Faina +2
New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for 853 <= q <= 4561 and q\in T1\cup T2 where T1={173,181,193,229,24…
New sizes of complete arcs in PG(2,q)
Alexander A. Davydov, Giorgio Faina, Stefano Marcugini +1
New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for 853<= q<= 2879 and q=3511,4096, 4523,5003,5347,5641,5843,6011. F…
Hyperfocused arcs in PG(2,32)
Giorgio Faina, Cristiano Parrettini, Fabio Pasticci
In PG(2,32) the following two results are proven by a computer aided search. (i) Uniqueness of hyperfocused 12-arcs, up to projectivities; (ii) Non-existence of hyperfocused 14-arc…