Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

Mapping Intimacies ◽

10.32920/ryerson.14662638 ◽

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.

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Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

10.32920/ryerson.14662638.v1 ◽

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

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Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians

Frames and Other Bases in Abstract and Function Spaces - Applied and Numerical Harmonic Analysis ◽

10.1007/978-3-319-55550-8_14 ◽

2017 ◽

pp. 333-353 ◽

Cited By ~ 5

Author(s):

Anna Breger ◽

Martin Ehler ◽

Manuel Gräf

Keyword(s):

Monte Carlo ◽

Function Approximation ◽

Monte Carlo Integration ◽

Quasi Monte Carlo

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Higher order Quasi-Monte Carlo integration for Bayesian PDE Inversion

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2018.09.019 ◽

2019 ◽

Vol 77 (1) ◽

pp. 144-172 ◽

Cited By ~ 5

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

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On Graph-Orthogonal Arrays by Mutually Orthogonal Graph Squares

Symmetry ◽

10.3390/sym12111895 ◽

2020 ◽

Vol 12 (11) ◽

pp. 1895 ◽

Cited By ~ 1

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.

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