Results 141 to 150 of about 10,083 (180)

The enumeration of cyclic mutually nearly orthogonal Latin squares

Journal of Combinatorial Designs, 2019
In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares.
Fatih Demirkale, Diane M Donovan, Janne I Kokkala   +2 more
exaly   +2 more sources

On the maximality of a set of mutually orthogonal Sudoku Latin Squares

Designs, Codes and Cryptography, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. D'haeseleer, K. Metsch, L. Storme, G. Voorde   +3 more
semanticscholar   +2 more sources

Mutually orthogonal latin squares: a brief survey of constructions

Journal of Statistical Planning and Inference, 2001
The authors provide a compendium of constructions of mutually orthogonal Latin squares (MOLS), concentrating on recursive constructions involving pairwise balanced designs and transversal designs. An updated table of lower bounds for \(N(n)\) is given, for \(1\leq n\leq 199\), where \(N(n)\) is the maximum number of Latin squares in a set of MOLS of ...
C. Colbourn, J. Dinitz
semanticscholar   +2 more sources

Difference Covering Arrays and Pseudo-Orthogonal Latin Squares [PDF]

Graphs and Combinatorics, 2015
Difference arrays are used in applications such as software testing, authentication codes and data compression. Pseudo-orthogonal Latin squares are used in experimental designs.
Fatih Demirkale, Diane M Donovan, Joanne Hall   +2 more
exaly   +4 more sources

Isometry invariant permutation codes and mutually orthogonal Latin squares

Journal of Combinatorial Designs, 2019
Commonly the direct construction and the description of mutually orthogonal Latin squares (MOLS) makes use of difference or quasi-difference matrices. Now there exists a correspondence between MOLS and separable permutation codes.
Ingo Janiszczak
exaly   +2 more sources

Four Mutually Orthogonal Latin Squares of Order 14

Journal of Combinatorial Designs, 2012
D. T. Todorov
exaly   +2 more sources

Concerning eight mutually orthogonal latin squares

Journal of Combinatorial Designs, 2006
AbstractIn this article, we provide a direct construction for 8 mutually orthogonal latin squares (MOLS)(48). Using this design together with one of Wilson's recursive constructions produces 8 new MOLS(v) for 88 other values of v. We also mention a few other new sets of 8 and 12 MOLS obtained recursively. © 2006 Wiley Periodicals, Inc. J Combin Designs
Abel, R. Julian R., Cavenagh, Nicholas
openaire   +1 more source

Improvements for lower bounds of mutually orthogonal Latin squares of sizes 54, 96 and 108

Designs, Codes and Cryptography
In this paper, respectively 8, 10 and 9 mutually orthogonal Latin squares (MOLS) of sizes n=54\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
R. J. R. Abel, I. Janiszczak, Reiner Staszewski   +2 more
semanticscholar   +1 more source

A Note on the Construction of Mutually Orthogonal Latin Squares

Biometrics, 1976
The construction of mutually orthogonal latin squares (MOLS) of side v when v is a prime power is well known (Bose, [19381). Methods of construction of mutually orthogonal latin squares for non-prime powers have been considered by many authors (MacNeish [1922], Mann [1942] and Raghavarao [19711).
Boob, B. S., Agrawal, H. L.
openaire   +1 more source

Orthogonal Latin Squares of Order Ten with Two Relations: A SAT Investigation

Discrete Mathematics, Algorithms and Applications (DMAA)
A k-net(n) is a combinatorial design equivalent to k - 2 mutually orthogonal Latin squares of order n. A relation in a net is a linear dependency over 𝔽 2 in the incidence matrix of the net.
Curtis Bright, Amadou Keita, Brett Stevens   +2 more
semanticscholar   +1 more source