Am × k matrixA, with entries from a set ofq ≧ 2 elements, is called an orthogonal arrayOA(m, k, q, t) (t ≧ 2) if eachm × t submatrix ofA contains all possible 1 ×t row vectors with the same frequencyλ(m = λq t). We call the array schematic if the set of rows ofA forms an association scheme with the relations determined by the Hamming distance. In this paper we determine the schematic orthogonal arraysOA(q t,k, q, t) with2t − 1 > k.
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Yoshizawa, M. On schematic orthogonal arraysOA(q t,k, q, t). Graphs and Combinatorics 3, 81–89 (1987). https://doi.org/10.1007/BF01788532
- Association Scheme