Visualization of the nets of type of Zaremba−Halton constructed in generalized number system

Abstract

In the present paper a class of two-dimensional nets Z κ,µ B2,ν of type of Zaremba-Halton constructed in generalized B2−adic system is introduced. In order to show their very well uniform distribution, we made their visualization with mathematical software Mathematica. In our paper ”On the (Vil,B2; α; γ)−diaphony of the nets of type of Zaremba - Halton constructed in generalized number system” we constructed a class Z κ,µ,B2,ν of two-dimensional nets (throughout this paper the term net will denote finite sequence) of type of Zaremba Halton. Also, the (Vil,B2; α; γ)−diaphony which is based on using two-dimensional Vilenkin functions constructed in the same B2−adic system,of the nets of the class Zκ,µ,B2,ν is investigated. The obtained results have theoretical character and treat to the influence of the parameter α to the exact order of the (Vil,B2; α; γ)−diaphony of the nets from the class Zκ,µ,B2,ν. The purpose of this paper is to present in extended form the visualization of some concrete nets from the class Zκ,µ, B2,ν and to show the distribution of the points of these nets. In this sense the reader can understand the distribution properties of the considered nets. To construct nets of the class Zκ,µ,B2,ν we use the mathematical software Mathematica. Our interest for the importance of these types of sequences is implied from their usage in numerical integration, construction of random number generators e.t.c.