A family of perpendicular arrays achieving perfect 4-fold secrecy

A perpendicular array PA,(t, k, u) is a n(y) by k array A of u distinct symbols, which satisfies: (i) every row of A contains k distinct symbols, (ii) for any t columns, and for any t distinct symbols, there are precisely 2 rows with the given symbols in the given columns. Such a structure may also be described as a A-uniform, t-homogeneous set of injective mappings from a k-set into a u-set. A close connection with t-designs is obvious. In contrast to the situation with designs, it is not clear if a perpendicular t-array PA,(t, k, u) is also a perpendicular s-array PA,,&, k, u) for SC t, where