A Library of Distance Distributions of Binary Orthogonal Arrays

A Library of Distance Distributions of Binary Orthogonal Arrays

Some bounds for MinD(M,n,2,t), MaxD(M,n,2,t) and CR(M,n,2,t) for some small values of M, n and t. Table 1.

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

Strength t=2

Index λ=1, OA.4.3.2.2
Index λ=2, OA.8.7.2.2
Index λ=3, OA.12.11.2.2
Index λ=4, OA.16.15.2.2
Index λ=5, OA.20.19.2.2
Index λ=6, OA.24.23.2.2
Index λ=7, OA.28.27.2.2
Index λ=8, OA.32.31.2.2
Index λ=9, OA.36.35.2.2
Index λ=10, OA.40.39.2.2

Strength t=3

Index λ=1, OA.8.4.2.3
Index λ=2, OA.16.8.2.3
Index λ=3, OA.24.12.2.3
Index λ=4, OA.32.16.2.3
Index λ=5, OA.40.20.2.3
Index λ=6, OA.48.24.2.3
Index λ=7, OA.56.28.2.3
Index λ=8, OA.64.32.2.3
Index λ=9, OA.72.36.2.3
Index λ=10, OA.80.40.2.3

Strength t=4

Index λ=1, OA.16.5.2.4
Index λ=2, OA.32.6.2.4
Index λ=4, OA.64.8.2.4
Index λ=6*, OA.96.11.2.4
Index λ=7*, OA.112.12.2.4
Index λ=8, OA.128.15.2.4
Index λ=10*, OA.160.16.2.4
Index λ=11*, OA.176.16.2.4
Index λ=12*, OA.192.17.2.4
Index λ=13*, OA.208.18.2.4
Index λ=14*, OA.224.19.2.4
Index λ=15*, OA.240.20.2.4
Index λ=16, OA.256.20.2.4

Strength t=5

Index λ=1, OA.32.6.2.5
Index λ=2, OA.64.7.2.5
Index λ=4, OA.128.9.2.5
Index λ=6*, OA.192.12.2.5
Index λ=7*, OA.224.13.2.5
Index λ=8, OA.256.16.2.5
Index λ=10*, OA.320.17.2.5
Index λ=11*, OA.352.17.2.5
Index λ=12*, OA.384.18.2.5
Index λ=13*, OA.416.19.2.5
Index λ=14*, OA.448.20.2.5
Index λ=15*, OA.480.21.2.5
Index λ=16, OA.512.21.2.5

Strength t=6

Index λ=1, OA.64.7.2.6
Index λ=2, OA.128.8.2.6
Index λ=4, OA.256.9.2.6
Index λ=6*, OA.384.10.2.6
Index λ=7*, OA.448.10.2.6
Index λ=8, OA.512.11.2.6
Index λ=12*, OA.768.12.2.6
Index λ=13*, OA.832.12.2.6
Index λ=14*, OA.896.12.2.6
Index λ=15*, OA.960.12.2.6
Index λ=16, OA.1024.15.2.6

Strength t=7

Index λ=1, OA.128.8.2.7
Index λ=2, OA.256.9.2.7
Index λ=4, OA.512.10.2.7
Index λ=6*, OA.768.11.2.7
Index λ=7*, OA.896.11.2.7
Index λ=8, OA.1024.12.2.7
Index λ=12*, OA.1536.13.2.7
Index λ=13*, OA.1664.13.2.7
Index λ=14*, OA.1792.13.2.7
Index λ=15*, OA.1920.13.2.7
Index λ=16, OA.2048.16.2.7

Strength t=8

Index λ=1, OA.256.9.2.8
Index λ=2, OA.512.10.2.8
Index λ=4, OA.1024.11.2.8
Index λ=6*, OA.1536.12.2.8
Index λ=7*, OA.1792.12.2.8
Index λ=8, OA.2048.12.2.8
Index λ=10*, OA.2560.13.2.8
Index λ=11*, OA.2816.13.2.8
Index λ=12*, OA.3072.13.2.8
Index λ=13*, OA.3328.13.2.8
Index λ=14*, OA.3584.13.2.8
Index λ=15*, OA.3840.13.2.8
Index λ=16, OA.4096.14.2.8

Strength t=9

Index λ=1, OA.512.10.2.9
Index λ=2, OA.1024.11.2.9
Index λ=4, OA.2048.12.2.9
Index λ=6*, OA.3072.13.2.9
Index λ=7*, OA.3584.13.2.9
Index λ=8, OA.4096.13.2.9
Index λ=10*, OA.5120.14.2.9
Index λ=11*, OA.5632.14.2.9
Index λ=12*, OA.6144.14.2.9
Index λ=13*, OA.6656.14.2.9
Index λ=14*, OA.7168.14.2.9
Index λ=15*, OA.7680.14.2.9
Index λ=16, OA.8192.15.2.9

Strength t=10

Index λ=1, OA.1024.11.2.10
Index λ=2, OA.2048.12.2.10
Index λ=4, OA.4096.13.2.10
Index λ=6*, OA.6144.14.2.10
Index λ=7*, OA.7168.14.2.10
Index λ=8, OA.8192.14.2.10
Index λ=11*, OA.11264.15.2.10
Index λ=12*, OA.12288.15.2.10
Index λ=13*, OA.13312.15.2.10
Index λ=14*, OA.14336.15.2.10
Index λ=15*, OA.15360.15.2.10
Index λ=16, OA.16384.15.2.10

Last update: December 13, 2021.