In 1986, Ryuzaburo Noda showed the following result based on Delsarte's theory on Hamming association schemes: If $A$ is an orthogonal array $(N, n, q, 3)$ achieving Rao's bound, then $A$ is either

(i) an orthogonal array $(2n, n, 2, 3)$ with $n \equiv 0$( (mod 4)), or

(ii) an orthogonal array $(q^{3}, q + 2, q, 3)$ with $q$ even.

We show the parameter $q$ in (ii) must be a multiple of 4 provided that $q$ is greater than 2. This is based on joint work with Alexander Gavrilyuk.

Bio: Sho Suda is an associate professor at the National Defense Academy of Japan. He got his master's degree at Kyushu University in 2008 under Professor Eiichi Bannai and his Ph.D. degree at Tohoku University in 2010 under Professor Akihiro Munemasa. He has been working on association schemes with connections to design theory.