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Encyclopaedia of DesignTheory: An orthogonal array |
Consider the following array with 12 rows and 4 columns:
| 0 | 0 | 0 | A |
| 0 | 0 | 0 | B |
| 0 | 0 | 0 | C |
| 0 | 1 | 1 | A |
| 0 | 1 | 1 | B |
| 0 | 1 | 1 | C |
| 1 | 0 | 1 | A |
| 1 | 0 | 1 | B |
| 1 | 0 | 1 | C |
| 1 | 1 | 0 | A |
| 1 | 1 | 0 | B |
| 1 | 1 | 0 | C |
In each of the first three columns, the symbols used are 0 and 1. In any two of these columns, each pair of symbols occurs exactly three times.
The last column contains the symbols A, B, C. Now if we pick the last column and any one other, then each pair of the relevant symbols occurs exactly twice.
For example, if we seek a 1 in column 2 and a B in column 4, this occurs in rows 5 and 11.
This orthogonal array does not have an index, since in different pairs of columns the numbers of occurrences of a pair of symbols are different.
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Peter J. Cameron
27 November 2002