Constructing Orthogonal Arrays on Non-abelian Groups

Author

Margaret Ann McComack, University of Wisconsin-MilwaukeeFollow

Date of Award

August 2013

Degree Type

Thesis

Degree Name

Master of Science

Department

Mathematics

First Advisor

Jay H. Beder

Committee Members

Yi Ming Zou, Richard Stockbridge

Abstract

For an orthogonal array (or fractional factorial design) on k factors, Xu and Wu (2001) define the array's generalized wordlength pattern (A₁, ..., A_k), by relating a cyclic group to each factor. They prove the property that the array has strength t if and only if A₁ = ... = A_t = 0. In their 2012 paper, Beder and Beder show that this result is independent of the group structure used. Non-abelian groups can be used if the assumption is made that the groups G_i are chosen so that the counting function O of the array is a class function on G.

The aim of this thesis is to construct examples of orthogonal arrays on G = G₁ x ... x G_k, where G is non-abelian, having two properties: given strength, and counting function O that is constant on the conjugacy classes of G.

Recommended Citation

McComack, Margaret Ann, "Constructing Orthogonal Arrays on Non-abelian Groups" (2013). Theses and Dissertations. 257.
https://dc.uwm.edu/etd/257