▁is ▁a ▁finite ▁field ▁of ▁order ▁q , ▁F q ▁( q ▁a ▁prime ▁power ) ▁and ▁the ▁rows ▁of ▁the ▁array ▁form ▁a ▁sub space ▁of ▁the ▁vector ▁space ▁( F q ) k . ▁ ▁Every ▁linear ▁orthogonal ▁array ▁is ▁simple . ▁ ▁Ex amples ▁ ▁An ▁example ▁of ▁a ▁ 2 -( 4 , ▁ 5 , ▁ 1 ) ▁orthogonal ▁array ; ▁a ▁strength ▁ 2 , ▁ 4 ▁level ▁design ▁of ▁index ▁ 1 ▁with ▁ 1 6 ▁runs . ▁ ▁An ▁example ▁of ▁a ▁ 2 -( 3 , 5 , 3 ) ▁orthogonal ▁array ▁( written ▁as ▁its ▁ ▁trans pose ▁for ▁ease ▁of ▁view ing ): ▁ ▁T rivial ▁examples ▁ ▁Any ▁t -( v , ▁t , ▁ λ ) ▁orthogonal ▁array ▁would ▁be ▁considered ▁trivial ▁since ▁they ▁are ▁easily ▁constructed ▁by ▁simply ▁listing ▁all ▁the ▁t - tu ples ▁of ▁the ▁v - set ▁ λ ▁times . ▁ ▁Mut ually ▁orthogonal ▁latin ▁squares ▁ ▁A ▁ 2 -( v , k , 1 ) ▁orthogonal ▁array ▁is ▁equivalent ▁to ▁a ▁set ▁of ▁k   −   2 ▁mut ually ▁orthogonal ▁latin ▁squares ▁of ▁order ▁v . ▁ ▁Index ▁one , ▁strength ▁ 2 ▁orthogonal ▁arrays ▁are ▁also ▁known ▁as ▁Hyper - G ra ec o - Lat in ▁square ▁designs ▁in ▁the ▁statistical ▁literature . ▁ ▁Let ▁A ▁be ▁a ▁strength ▁ 2 , ▁index ▁ 1 ▁orthogonal ▁array ▁on ▁a ▁v - set ▁of ▁elements , ▁identified ▁with ▁the ▁set ▁of