Covering arrays for words of length t over a d letter alphabet are k × n arrays with entries from the alphabet so that for each choice of t columns, each of the dt t-letter words appears at least once among the rows of the selected columns. We study two schemes in which all words are not considered to be different. In the first case, words are equivalent if they induce the same partition of a t element set. In the second case, words of the same weighted sum are equivalent. In both cases we produce logarithmic upper bounds on the minimum size k = k(n) of a covering array. Most definitive results are for t = 2, 3, 4.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:honors-1492 |
| Date | 01 May 2018 |
| Creators | Cassels, Joshua, Godbole, Anant |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Undergraduate Honors Theses |
| Rights | Copyright by the authors., http://creativecommons.org/licenses/by-nc-nd/3.0/ |
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