LS-successioni di punti nel quadrato

الأصل · EN

The main purpose of this master thesis is to study the LS-sequences of points introduced by Carbone in Carbone and find two generalizations of them to the unit square. Here we also present a new algorithm proposed by the same author in Carbone2 and we implement it in order to have a graphical description of these sequences. Chapter 1 includes a collection of results concerning the uniform ditribution theory and the discrepancy (we refer to Drmotaₜichy and Kuipersₙiederreiter for a complete survey on the matter). In Chapter 2 we focuse our attention on the LS-sequences of partitions and of points in the unit interval, giving particular attention to the ordering of the points "à la van der Corput and finding a way to compute them related to the digit expansion of natural numbers in base L+S. In Chapter 3 we move on the unit square where we find two generalizations of the LS-sequences following the historical development of the van der Corput sequence in the multidimensional case. This is the reason why we call the first sequence LS- sequence of points à la van der Corput-Hammersley and the second one LS-sequence à la Halton.