The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less

A computer generation of all pairs of mutually orthogonal Latin squares of order ten and dimension 35 or less is undertaken. All such pairs are successfully generated up to main class equivalence. No pairs of mutually orthogonal Latin squares of order ten exist for dimension 33. Six dimension 34...

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Main Author:	Delisle, Erin
Other Authors:	Myrvold, W. J.
Language:	English en
Published:	2010
Subjects:	mutually orthogonal Latin squares backtracking UVic Subject Index::Sciences and Engineering::Applied Sciences::Computer science
Online Access:	http://hdl.handle.net/1828/2964

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spelling	ndltd-uvic.ca-oai-dspace.library.uvic.ca-1828-29642015-01-29T16:51:27Z The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less Delisle, Erin Myrvold, W. J. mutually orthogonal Latin squares backtracking UVic Subject Index::Sciences and Engineering::Applied Sciences::Computer science A computer generation of all pairs of mutually orthogonal Latin squares of order ten and dimension 35 or less is undertaken. All such pairs are successfully generated up to main class equivalence. No pairs of mutually orthogonal Latin squares of order ten exist for dimension 33. Six dimension 34 pairs, which are counterexamples to a conjecture by Moorehouse, are found. Eighty-five pairs can be formed with dimension 35. None of the pairs can be extended to a triple. If a triple of mutually orthogonal Latin squares exists for order ten, the pairs of Latin squares in the triple must be of dimension 36 or 37. 2010-08-24T20:19:13Z 2010-08-24T20:19:13Z 2010 2010-08-24T20:19:13Z Thesis http://hdl.handle.net/1828/2964 English en Available to the World Wide Web
collection	NDLTD
language	English en
sources	NDLTD
topic	mutually orthogonal Latin squares backtracking UVic Subject Index::Sciences and Engineering::Applied Sciences::Computer science
spellingShingle	mutually orthogonal Latin squares backtracking UVic Subject Index::Sciences and Engineering::Applied Sciences::Computer science Delisle, Erin The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less
description	A computer generation of all pairs of mutually orthogonal Latin squares of order ten and dimension 35 or less is undertaken. All such pairs are successfully generated up to main class equivalence. No pairs of mutually orthogonal Latin squares of order ten exist for dimension 33. Six dimension 34 pairs, which are counterexamples to a conjecture by Moorehouse, are found. Eighty-five pairs can be formed with dimension 35. None of the pairs can be extended to a triple. If a triple of mutually orthogonal Latin squares exists for order ten, the pairs of Latin squares in the triple must be of dimension 36 or 37.
author2	Myrvold, W. J.
author_facet	Myrvold, W. J. Delisle, Erin
author	Delisle, Erin
author_sort	Delisle, Erin
title	The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less
title_short	The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less
title_full	The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less
title_fullStr	The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less
title_full_unstemmed	The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less
title_sort	search for a triple of mutually orthogonal latin squares of order ten: looking through pairs of dimension thirty-five and less
publishDate	2010
url	http://hdl.handle.net/1828/2964
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The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less

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