Orthogonal Arrays of Strength 3

A new construction for orthogonal arrays of strength 3 is given. 1 Introduction An orthogonal array of size N , degree k, order s and strength t is a k by N array with entries from a set of s 2 symbols, having the property that in every t by N subarray, every t by 1 column array appears the same number = N s t times. We denote such an array by OA (t; k; s). The parameter is called the index of the array. Existence results for orthogonal arrays of strength greater than or equal to three are few and far between. A summary of these results is given in [3]. For t = 3, the best known upper bound on k for fixed and s is the Bose-Bush bound [2]: k $ s 2 \Gamma 1 s \Gamma 1 \Gamma 1 % : A improvement is obtained when \Gamma 1 j b (mod s \Gamma 1) and 1 ! b ! s \Gamma 1: k $ s 2 \Gamma 1 s \Gamma 1 % \Gamma 6 6 6 4 q 1 + 4s(s \Gamma 1 \Gamma b) \Gamma (2s \Gamma 2b \Gamma 1) 2 7 7 7 5 : In [5] orthogonal arrays of strength 2 were constructed by applying a 2-transit..