scholarly journals Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

2021 ◽  
Author(s):  
Tamar Krikorian
Keyword(s):  
Orthogonal Arrays ◽  
Latin Squares ◽  
Monte Carlo Integration ◽  
Combinatorial Method ◽  
Covering Arrays ◽  
Combinatorial Objects ◽  
Quasi Monte Carlo ◽  
Combinatorial Constructions ◽  
Ordered Orthogonal Arrays ◽  
Combinatorial Methods

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

scholarly journals Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

2021 ◽  
Author(s):  
Tamar Krikorian
Keyword(s):  
Orthogonal Arrays ◽  
Latin Squares ◽  
Monte Carlo Integration ◽  
Combinatorial Method ◽  
Covering Arrays ◽  
Combinatorial Objects ◽  
Quasi Monte Carlo ◽  
Combinatorial Constructions ◽  
Ordered Orthogonal Arrays ◽  
Combinatorial Methods

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion

2019 ◽  
Vol 77 (1) ◽  
pp. 144-172 ◽  
Author(s):  
Josef Dick ◽  
Robert N. Gantner ◽  
Quoc T. Le Gia ◽  
Christoph Schwab
Keyword(s):  
Monte Carlo ◽  
Higher Order ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo

scholarly journals On Graph-Orthogonal Arrays by Mutually Orthogonal Graph Squares

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1895 ◽  
Author(s):  
M. Higazy ◽  
A. El-Mesady ◽  
M. S. Mohamed
Keyword(s):  
Computer Science ◽  
Finite Fields ◽  
Orthogonal Array ◽  
Orthogonal Arrays ◽  
Latin Squares ◽  
Error Correcting Codes ◽  
Recursive Construction ◽  
Orthogonal Latin Squares ◽  
Mutually Orthogonal Latin Squares ◽  
Definition Of

During the last two centuries, after the question asked by Euler concerning mutually orthogonal Latin squares (MOLS), essential advances have been made. MOLS are considered as a construction tool for orthogonal arrays. Although Latin squares have numerous helpful properties, for some factual applications these structures are excessively prohibitive. The more general concepts of graph squares and mutually orthogonal graph squares (MOGS) offer more flexibility. MOGS generalize MOLS in an interesting way. As such, the topic is attractive. Orthogonal arrays are essential in statistics and are related to finite fields, geometry, combinatorics and error-correcting codes. Furthermore, they are used in cryptography and computer science. In this paper, our current efforts have concentrated on the definition of the graph-orthogonal arrays and on proving that if there are k MOGS of order n, then there is a graph-orthogonal array, and we denote this array by G-OA(n2,k,n,2). In addition, several new results for the orthogonal arrays obtained from the MOGS are given. Furthermore, we introduce a recursive construction method for constructing the graph-orthogonal arrays.

Quasi-Monte Carlo Integration

1995 ◽  
Vol 122 (2) ◽  
pp. 218-230 ◽  
Author(s):  
William J. Morokoff ◽  
Russel E. Caflisch
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Integration ◽  
Quasi Monte Carlo

scholarly journals Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

2015 ◽  
Vol 32 (4) ◽  
pp. 1353-1374 ◽  
Author(s):  
Fatih Demirkale ◽  
Diane Donovan ◽  
Joanne Hall ◽  
Abdollah Khodkar ◽  
Asha Rao
Keyword(s):  
Latin Squares ◽  
Covering Arrays ◽  
Orthogonal Latin Squares
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