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 order 48
โ Scribed by Mieczyslaw Wojtas
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 103 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
โฆ Synopsis
A direct construction of six mutually orthogonal Latin squares of order 48 is given.
๐ SIMILAR VOLUMES
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
In this article we give some new constructions of self-conjugate self-orthogonal diagonal Latin squares (SCSODLS). As an application of such constructions, we give a conclusive result regarding the existence of SCSODLS and show that there exists an SCSODLS of order n if and only if n โก 0, 1 (mod 4),
A construction for a row-complete latin square of order n, where n is any odd composite number other than 9, is given in this article. Since row-complete latin squares of order 9 and of even order have previously been constructed, this proves that row-complete latin squares of every composite order