Taguchi's catalog of orthogonal arrays is based on the mathematical theory of factorial designs and difference sets developed by R. C. Bose and his associates. These arrays evolved as extensions of factorial designs and latin squares. This paper (1) describes the structure and constructions of Taguchi's orthogonal arrays, (2) illustrates their fractional factorial nature, and (3) points out tha...

Two Latin squares of order n are orthogonal if in their superposition, each of the n ordered pairs of symbols occurs exactly once. Colbourn, Zhang and Zhu, in a series of papers, determined the integers r for which there exist a pair of Latin squares of order n having exactly r different ordered pairs in their superposition. Dukes and Howell defined the same problem for Latin squares of differe...

We give an exact characterization of permutation polynomials mod ulo n w w a polynomial P x a a x adx d with integral coe cients is a permutation polynomial modulo n if and only if a is odd a a a is even and a a a is even We also characterize polynomials de ning latin squares mod ulo n w but prove that polynomial multipermutations that is a pair of polynomials de ning a pair of orthogonal latin...

Much has been written about the construction of sets of mutually orthogonal latin squares (MOLS). In [8], a lengthy survey of these constructions is given. Existence of MOLS is tabulated in [1], historical information appears in [9, 21], and proofs of many of the existence results appear in [1, 4, 21]. Rather than repeat these surveys here, we instead explore how some of the available construct...

Heinrich, K., L. Wu and L. Zhu, Incomplete self-orthogonal latin squares ISOLS(6m + 6, 2m) exist fo all m, Discrete Mathematics 87 (1991) 281-290. An incomplete self-orthogonal latin square of order v with an empty subarray of order n, an ISOLS(v, n) can exist only if v 2 3n + 1. We show that an ISOLS(6m + 6, 2m) exists for all values of m and thus only the existence of an ISOLS(6m + 2,2m), m 2...

We consider orthogonal arrays of strength two and even order q having n columns which are equivalent to n − 2 mutually orthogonal Latin squares of order q. We show that such structures induce graphs on n vertices, invariant up to complementation. Previous methods worked only for single Latin squares of even order and were harder to apply. If q is divisible by four the invariant graph is simple ...

We study compositional inverses of permutation polynomials, complete map-pings, mutually orthogonal Latin squares, and bent vectorial functions. Recently it was obtained in [33] the compositional inverses of linearized permutation binomials over finite fields. It was also noted in [29] that computing inverses of bijections of subspaces have applications in determining the compositional inverses...