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Bounds on the maximum number of Latin squares in a mutually quasi-orthogonal set [PDF]
Discrete Mathematics, 2001 In this paper we are concerned with finding an upper bound on Nq(n), the maximum number of Latin squares of order n in a mutually quasi-orthogonal set. In doing so, we make use of relationships with orthogonal frequency squares, equidistant permutation ...
Roger Whitaker
exaly +3 more sources
Pairwise "Orthogonal Generalized Room Squares" and Equidistant Permutation Arrays [PDF]
Journal of Combinatorial Theory, 1978 A generalized Room square S ( r , λ ; v ) is an r × r array such that every cell in the array contains a subset of a v -set V . This subset could of course be the empty set.
S. Vanstone
semanticscholar +2 more sources
Difference Covering Arrays and Pseudo-Orthogonal Latin Squares [PDF]
Graphs and Combinatorics, 2015 A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all.
Asha Rao +2 more
exaly +3 more sources
A novel application on mutually orthogonal graph squares and graph-orthogonal arrays
AIMS Mathematics, 2022 Security of personal information has become a major concern due to the increasing use of the Internet by individuals in the digital world. The main purpose here is to prevent an unauthorized person from gaining access to confidential information.
A. El-Mesady +2 more
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Mutually Orthogonal Sudoku Latin Squares and Their Graphs [PDF]
Graphs and Combinatorics, 2021 We introduce a graph attached to mutually orthogonal Sudoku Latin squares. The spectra of the graphs obtained from finite fields are explicitly determined. As a corollary, we then use the eigenvalues to distinguish non-isomorphic Sudoku Latin squares.
Sho Kubota, Sho Suda, Akane Urano
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A general construction method for component orthogonal arrays
Quality and Reliability Engineering International, 2023 Order‐of‐addition (OofA) experiments have gained renewed attention in recent years, especially in regard to their design. For these experiments, the response is determined by the order in which components are added.
Chunyan Wang +2 more
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Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares
Bhartiya Krishi Anusandhan Patrika, 2022 t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t treatments (t ≥ 2) occur together is a constant.
Sayantani Karmakar +4 more
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On Graph-Orthogonal Arrays by Mutually Orthogonal Graph Squares
Symmetry, 2020 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.
M. Higazy, A. El-Mesady, M. S. Mohamed
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On generalized strong complete mappings and mutually orthogonal Latin squares
Ars Math. Contemp., 2021 We present an application of generalized strong complete mappings to construction of a family of mutually orthogonal Latin squares. We also determine a cycle structure of such mapping which form a complete family of MOLS.
A. Muratovic-Ribic
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Cycles of quadratic Latin squares and antiperfect 1‐factorisations [PDF]
Journal of combinatorial designs (Print), 2023 A Latin square of order n $n$ is an n × n $n\times n$ matrix of n $n$ symbols, such that each symbol occurs exactly once in each row and column. For an odd prime power q $q$ let F q ${{\mathbb{F}}}_{q}$ denote the finite field of order q $q$ .
J. Allsop
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