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Title: Geometric orthogonal arrays: Multidimensional space filling property and construction via factor collapse Authors:  Frederick Kin Hing Phoa - Academia Sinica (Taiwan) [presenting]
Cheng-Yu Sun - Simon Fraser University (Canada)
Shao-Wei Cheng - National Tsing Hua University (Taiwan)
Abstract: A new class of space-filling designs optimized under a new multi-dimensional space-filling property is introduced which is called {\it geometric strength}. We propose a systematic construction method via techniques in Galois field for this new class of designs. The factor levels in a regular design are collapsed and the strength of the collapsed design is enhanced. The reversed process to relabel factor levels of the regular design improves its space-filling property. This method is more efficient than the existing methods via level permutations, especially when the number of factor levels is large. When two collapsers are indistinguishable in terms of the strength of the collapsed designs, we propose a new criterion called maximal strength efficiency. It not only maximizes the strength of the collapsed design, but also maximizes the proportion of the projected sub-designs that are full factorials.