Complete $$\varvec{(k,4)}$$ ( k , 4 ) -arcs from quintic curves

Bartoli, Daniele; Speziali, Pietro; Zini, Giovanni

doi:10.1007/s00022-017-0390-2

Cited by 6 publications

(9 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The statistic of this process is shown in Table 10. (15,4)-arcs is 185. The statistic of this process is given in Table 11.…”

Section: )-Arcsmentioning

confidence: 96%

“…The number of (7,4)-arcs 7 that have been constructed is 287. Among these arcs, the number of distinct (7,4) {2, 3, 7, 113, 182}…”

Section: (74)-arcsmentioning

confidence: 99%

“…The statistic of this process is given in Table 11. The number of (16,4)-arcs 16 is 41107 and the number of distinct (16,4)-arcs is 237. The statistic of this process is given in Table 12.…”

Section: )-Arcsmentioning

confidence: 99%

“…For example, the first step begins from the set . Then, the second step is to construct the number of (7,4)-arcs. This construction is made by adding separately to all the points from the lines of (2,17), = 1,…,307 that satisfy ∩ = 4.…”

Section: Introductionmentioning

confidence: 99%

“…Then the -secant distribution for each arc is calculated and then among these classes, the distinct classes of -secant distribution with their associated arcs are chosen only. So, the number of distinct (7,4)-arcs is based on the number of distinct classes of secant distribution. All the details of this method are illustrated in section of research method.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A complete (48, 4)-arc in the Projective Plane Over the Field of Order Seventeen

Hamed

Hirschfeld

2021

Baghdad Sci.J

View full text Add to dashboard Cite

The article describes a certain computation method of ( , )-arcs to construct the number of distinct ( , 4)-arcs in PG(2,17) for = 7, … ,48. In this method, a new approach employed to compute the number of ( , )-arcs and the number of distinct ( , )-arcs respectively. This approach is based on choosing the number of inequivalent classes { 4 , 3 , 2 , 1 , 0 } of -secant distributions that is the number of 4-secant, 3secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of ( , 4)-arc that has been constructed by this method is = 48. The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of ( , )-arcs in each construction especially for large value of and then reduce the running time of the calculation. Therefore, it allows to decrease the memory storage for the calculation processes. This method's effectiveness evaluation is confirmed by the results of the calculation where a largest size of complete ( , 4)-arc is constructed. This research's calculation results develop the strategy of the computational approaches to investigate big sizes of ( , )-arcs in (2, ) where it put more attention to the study of the number of the inequivalent classes of -secants of ( , )-arcs in (2, ) which is an interesting aspect. Consequently, it can be used to establish a large value of .

show abstract

“…The statistic of this process is shown in Table 10. (15,4)-arcs is 185. The statistic of this process is given in Table 11.…”

Section: )-Arcsmentioning

confidence: 96%

“…The number of (7,4)-arcs 7 that have been constructed is 287. Among these arcs, the number of distinct (7,4) {2, 3, 7, 113, 182}…”

Section: (74)-arcsmentioning

confidence: 99%

Section: )-Arcsmentioning

confidence: 99%