Concerning seven and eight mutually orthogonal Latin squares

R. Julian; Charles Colbourn; Charles J. Colbourn; Mieczyslaw Wojtas

doi:10.1002/jcd.10070

Concerning seven and eight mutually orthogonal Latin squares

R. Julian, Charles Colbourn, Charles J. Colbourn, Mieczyslaw Wojtas

Computer Science and Engineering

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 1419.

Original language	English (US)
Pages (from-to)	123-131
Number of pages	9
Journal	Journal of Combinatorial Designs
Volume	12
Issue number	2
DOIs	https://doi.org/10.1002/jcd.10070
State	Published - 2004

Keywords

Difference matrix
MOLS
Quasi-difference matrix
Transversal design

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Access to Document

10.1002/jcd.10070

Cite this

@article{19c53f5987af4333b44ff00c06fc3a6a,

title = "Concerning seven and eight mutually orthogonal Latin squares",

abstract = "In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 1419.",

keywords = "Difference matrix, MOLS, Quasi-difference matrix, Transversal design",

author = "R. Julian and Charles Colbourn and Colbourn, {Charles J.} and Mieczyslaw Wojtas",

year = "2004",

doi = "10.1002/jcd.10070",

language = "English (US)",

volume = "12",

pages = "123--131",

journal = "Journal of Combinatorial Designs",

issn = "1063-8539",

publisher = "John Wiley and Sons Inc.",

number = "2",

}

TY - JOUR

T1 - Concerning seven and eight mutually orthogonal Latin squares

AU - Julian, R.

AU - Colbourn, Charles

AU - Colbourn, Charles J.

AU - Wojtas, Mieczyslaw

PY - 2004

Y1 - 2004

N2 - In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 1419.

AB - In this paper, three new direct Mutually Orthogonal Latin Squares (MOLS) constructions are presented for 7 MOLS(24), 7 MOLS(75) and 8 MOLS(36); then using recursive methods, several new constructions for 7 and 8 MOLS are obtained. These reduce the largest value for which 7 MOLS are unknown from 780 to 570, and the largest odd value for which 8 MOLS are unknown from 1935 to 1419.

KW - Difference matrix

KW - MOLS

KW - Quasi-difference matrix

KW - Transversal design

UR - http://www.scopus.com/inward/record.url?scp=1542274573&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542274573&partnerID=8YFLogxK

U2 - 10.1002/jcd.10070

DO - 10.1002/jcd.10070

M3 - Article

AN - SCOPUS:1542274573

SN - 1063-8539

VL - 12

SP - 123

EP - 131

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 2

ER -

Concerning seven and eight mutually orthogonal Latin squares

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this