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Four pairwise orthogonal latin squares of order 24

โœ Scribed by Robert Routh; Matthew Peters


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
219 KB
Volume
44
Category
Article
ISSN
0097-3165

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Five mutually orthogonal Latin squares o
โœ Mieczyslaw Wojtas ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 120 KB

Let N(n) denote the maximum number of mutually orthogonal Latin squares of order n. It is proved that N(24) and N(40)>~5.

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Let N ( n ) denote the maximum number of mutually orthogonal Latin squares of order n. It is shown that N(35) 2 5.

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A direct construction of six mutually orthogonal Latin squares of order 48 is given.

Embedding a latin square in a pair of or
โœ Peter Jenkins ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 123 KB

## Abstract In this paper, it is shown that a latin square of order __n__ with __n__โ€‰โ‰ฅโ€‰3 and __n__โ€‰โ‰ โ€‰6 can be embedded in a latin square of order __n__^2^ which has an orthogonal mate. A similar result for idempotent latin squares is also presented. ยฉ 2005 Wiley Periodicals, Inc. J Combin Designs 1

Existence of conjugate orthogonal diagon
โœ F. E. Bennett; B. Du; H. Zhang ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 151 KB ๐Ÿ‘ 1 views

We shall refer to a diagonal Latin square which is orthogonal to its (3, 2, 1)-conjugate and having its (3, 2, 1)-conjugate also a diagonal Latin square as a (3, 2, 1)-conjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS and it is found that it c