# A Library of Distance Distributions of Ternary Orthogonal Arrays

• Some bounds for MinD(M,n,3,t), MaxD(M,n,3,t) and CR(M,n,3,t) for some small values of M, n and t. Table 2.

• File names: The file OA.M.n.q.t.txt corresponds to OA(M,n,q,t).

• The name represents an orthogonal array with M runs, n factors, q levels, and strength t. This is an array (a matrix) of size M by n, with entries from 0 to q-1, with the property that in any t columns you see each of the q^t possibilities equally often.

• For a given orthogonal array C denote by λ = M/q^t the index, d(C) the minimum distance, and ρ(C) the covering radius, respectively.

• DD in file sorted - [d0, d1, ... , dn].

• The number of DD for internal points / the number of DD for all points: # Internal / # All.

• For an introduction to orthogonal arrays see the book Orthogonal Arrays: Theory and Applications by Hedayat, Sloane and Stufken.

• Neil Sloane's web page: A Library of Orthogonal Arrays.

• Complete series of non-isomorphic orthogonal arrays, P. Eendebak, E. Schoen.

 OA(M,n,q=3,t) λ, # Internal / # All d(C), ρ(C) After reduction: # Internal / # All d(C), ρ(C) ↙    ↘ OA(M/3,n-1,3,t-1) OA(2M/3,n-1,3,t-1) ↙     ↘ ↙     ↘ OA(M/3^2,n-2,3,t-2) OA(2M/3^2,n-2,3,t-2) OA(2^2 M/3^2,n-2,3,t-2) ↙     ↘ ↙     ↘ ↙     ↘ OA(M/3^3,n-3,3,t-3) OA(2 M/3^3,n-3,3,t-3) OA(2^2 M/3^3,n-3,3,t-3) OA(2^3 M/3^3,n-3,3,t-3) ↙     ↘ ↙     ↘ ↙     ↘ ↙     ↘ OA(M/3^4,n-4,3,t-4) OA(2 M/3^4,n-4,3,t-4) OA(2^2 M/3^4,n-4,3,t-4) OA(2^3 M/3^4,n-4,3,t-4) OA(2^4 M/3^4,n-4,3,t-4) . . .

Strength t=2

Strength t=3

Strength t=4

Strength t=5

Strength t=6

Strength t=7

Strength t=8

Strength t=9

Strength t=10

Last update: October 25, 2021.