[R] Mutually Orthogonal Latin Squares

Robin Hankin r.hankin at noc.soton.ac.uk
Fri Apr 21 09:50:07 CEST 2006

Hi Jinsong

Finding even a pair of mutually orthogonal latin squares for
arbitrary order is a difficult problem.  For example, Euler
conjectured that no orthogonal latin squares exist for order
4n+2; this was only disproved in 1960 (in 1900 it
was proved that  there are none of order 6). . . . evidently
a complicated research topic!

Now, this doesn't quite answer your question, but functions
panmagic.4(), panmagic.8() and magic.8() of the magic package
use Latin squares of sizes 4 and 8 for their construction.



On 20 Apr 2006, at 16:36, Jinsong Zhao wrote:

> Hi all,
> The package crossdes could contruct a complete sets of mutually  
> orthogonal latin squares.
> The construction works for prime powers only.
> I hope to know whether there is a way to construct a mutually  
> orthogonal Lation square for
> 10 or other numbers that could not be prime powers.
> Thanks for any suggestions.
> Best wishes,
> Jinsong Zhao
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Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

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