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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Mutually orthogonal latin squares based on ℤ<sub>3</sub>× ℤ<sub>9</sub>

Carter, James Michael 17 August 2007 (has links)
No description available.
2

Mutually quasi-orthogonal Latin squares

Whitaker, Roger Marcus January 1999 (has links)
This thesis considers problems concerning Latin squares and sets of mutually quasiorthogonal Latin squares (MQOLS). We show how MQOLS are related to a number of other designs and establish bounds on Nq(n), the maximum number of Latin squares of order n in a mutually quasi-orthogonal set. We report the number of quasi-complete mappings admitted by each group of order 15 or less, and explain the surprising result that each of the non-cyclic groups of order 8 possesses exactly 384 complete mappings. For each group G of order 15 or less, we identify the sizes of all maximal sets of mutually orthogonal orthomorphisms. We also identify a number of new maximal sets for larger groups. We present a method to determine all proper, maximal sets of MQOLS of order n and carry this out for n < 6. Also we present a search for 3 MQOLS of order 10, which, whilst not identifying such a set, led to the identification of all resolutions of each (10,3, 2)-balanced incomplete block design. We give a construction for MQOLS based on groups, and use this to determine new sets of 2n - 1 MQOLS of order 2n based on two infinite classes of group. Existence results for MQOLS based on groups are also extended. Two constructions for (n x n)/k semi-Latin squares are given, one of which provides some new A-, D- and E-optimal examples with k > n which out-perform the existing A-, D- and E-optimal examples in the E'-criteria. Finally we consider the problem of determining invertible directed terraces of each non-abelian group of order < 21, and in so doing construct the first doubly balanced bipartite tournament of odd order.

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