Series of Arrays

jointly authored with Pieter Eendebak (Dept. of Engineering Management, University of Antwerp, Belgium)

On the orthogonal array pages of Pieter Eendebak, we present numbers of isomorphism classes for many series of orthogonal arrays. For example, the entry on strength-3 arrays of 64 runs, two four-level factors and any number of two-level factors is:

OA(64; 3; 4^2 2^a) : 12, 267, 13903, 104949, 175297, 151708, 138825, 83409, 35807, 10030, 2159, 0

There is just one 4^2 2^1 design in the series, which has all factor level combinations repeated twice. The numbers 12, 267, … , 2159, 0 show the different arrays for 2…13 factors. The subpage for this particular series then gives additional details, such as some explicit arrays and a picture of the numbers of arrays as a function of the total number of factors, or columns, reproduced below.


Most of the arrays are generated by Pieter’s Orthogonal Arrays program, some series are generated by hand. The algorithm used is described in our paper Complete Enumeration of Pure-Level and Mixed-Level Orthogonal Arrays, which appeared in the Journal of Combinatorial Designs 18 (2010): 123-140.

In many cases, we include a few of the best arrays on the site. However, it is undoable to give many more than a few, especially for the larger series on the site, because this would take several GB of data storage. If you want to study generated arrays that are not explicitly given on the site, please contact one of us.