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Concerning seven and eight mutually orthogonal Latin squares

โœ Scribed by R. Julian R. Abel; Charles J. Colbourn; Mieczyslaw Wojtas

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
97 KB
Volume
12
Category
Article
ISSN
1063-8539

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โœฆ Synopsis

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 419. ยฉ 2003 Wiley Periodicals, Inc.

๐Ÿ“œ SIMILAR VOLUMES

Concerning eight mutually orthogonal lat
Concerning eight mutually orthogonal latin squares
โœ R. Julian R. Abel; Nicholas Cavenagh ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 83 KB

## Abstract In 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 ob

On seven mutually orthogonal Latin squar
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โœ Mieczyslaw Wojtas ๐Ÿ“‚ Article ๐Ÿ“… 1977 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 727 KB

Let N(n) denote the maximum numner of mutually orthogonal Latin squares of order n. II is shown that N(n) 3 7 for n > 4922.

Five mutually orthogonal Latin squares o
Five mutually orthogonal Latin squares of order 35
โœ Mieczyslaw Wojtas ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 73 KB ๐Ÿ‘ 1 views

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

Six mutually orthogonal Latin squares of
Six mutually orthogonal Latin squares of order 48
โœ Mieczyslaw Wojtas ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 103 KB ๐Ÿ‘ 1 views

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