On the OA(1536,13,2,7) and related orthogonal arrays

摘要

With a computer-aided approach based on connection with equitable partitions, we establish the uniqueness of the orthogonal array OA (1536, 13, 2, 7), constructed in Fon-Der-Flaass (2017) as an equitable partition of the 13-cube with quotient matrix [[0, 13], [3, 10]]. By shortening the OA(1536, 13, 2, 7), we obtain 3 inequivalent orthogonal arrays OA(768, 12, 2, 6), which is a complete classification for these parameters too.