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.
Four pairwise orthogonal latin squares of order 24
โ 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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๐ SIMILAR VOLUMES
Let N ( n ) denote the maximum number of mutually orthogonal Latin squares of order n. It is shown that N(35) 2 5.
A direct construction of six mutually orthogonal Latin squares of order 48 is given.
## Abstract In this paper, it is shown that a latin square of order __n__ with __n__โโฅโ3 and __n__โโ โ6 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
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