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Abstract:
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Mixed orthogonal arrays of strength two and size s^{mn} are constructed by grouping points in the finite projective geometry PG(mn-1,s). PG(mn-1,s) can be partitioned into (s^{mn}-1)/(s^n-1) (n-1)-flats such that each (n-1)-flat is associated with a point in PG(m-1,s^n). A set of (s^t-1)/(s-1) points in PG(m-1,s^n) is called a (t-1)-flat over GF(s) if it is isomorphic to PG(t-1,s). If there exists a (t-1)-flat over GF(s) in PG(m-1, s^n), then we can replace (s^t-1)/(s-1) s^n-level columns in an orthogonal array by (s^n-1)/(s-1) s^t-level columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. New orthogonal arrays of sizes 256, 512, and 1024 are also obtained using PG(6,2), PG(7,2), and PG(8,2) respectively.
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