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 OJS  Vol.2 No.2 , April 2012
On a Grouping Method for Constructing Mixed Orthogonal Arrays
Chung-Yi Suen
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Abstract: Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-1)-flat is associated with a point in PG(m-1, sn). An orthogonal array Lsmn((sn)(smn-)(sn-1) can be constructed by using (smn-1)/( sn-1) points in PG(m-1, sn). A set of (st-1)/(s-1) points in PG(m-1, sn) 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, sn), then we can replace the corresponding [(st-1)/(s-1)] sn-level columns in Lsmn((sn)(smn-)(sn-1) by (smn-1)/( sn-1) st -level columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. In this paper, we study methods for finding disjoint (t-1)-flats over GF(s) in PG(m-1, sn) in order to construct more mixed orthogonal arrays of strength two. In particular, if m and n are relatively prime then we can construct an Lsmn((sm)smn-1/sm-1-i(sn-1)/ (s-1)( sn) i(sm-1)/ s-1) for any 0
Keywords: Finite field; Finite projective geometry; (t-1)-flat over GF(s) in PG(m-1, sn ); Geometric orthogonal array; Matrix representation; Minimal polynomial; Orthogonal main-effect plan; Primitive element; Tight.
Cite this paper: C. Suen, "On a Grouping Method for Constructing Mixed Orthogonal Arrays," Open Journal of Statistics, Vol. 2 No. 2, 2012, pp. 188-197. doi: 10.4236/ojs.2012.22022.
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