A construction and decomposition of orthogonal arrays with non-prime-power numbers of symbols on the complement of a Baer subplane

Fuji-Hara and Kamimura (Util Math 43: 65-70, 1993) outlined a method for constructing orthogonal arrays of strength 2 on the complement of a Baer subplane, with q(q-1) symbols for a prime power q. In this paper, we demonstrate that these orthogonal arrays can be decomposed into other orthogonal arrays of strength 2, with the same numbers of constraints and symbols but with smaller sizes and indices. In our construction, each orthogonal array of the decomposition can be obtained as an orbit of the point-set of a Baer subplane, under the action of a certain projective linear group. Furthermore, for q = 2 (mod 3) and q > 2, a series of the new orthogonal arrays cannot be obtained by Bush's direct product construction, which is a classical method for constructing orthogonal arrays with non-prime-power numbers of symbols.