A Library of Distance Distributions of Ternary Orthogonal Arrays

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.