Journal of Statistical Theory and Practice

, Volume 1, Issue 3–4, pp 299–309 | Cite as

Hilbert Bases for Orthogonal Arrays

  • Enrico CarliniEmail author
  • Giovanni Pistone


In this paper, we relate the problem of generating all 2-level orthogonal arrays of given dimension and strength, i.e. elements in OA (N,2n,m), where N is the number of rows, n is the number of factors, and m the strength, to the solution of an integer programming problem involving rational convex cones. We admit any number of replications in the arrays, i.e. we consider not only set but also multi-set. This problem can be theoretically solved by means of Hilbert bases which form a finite generating set for all the elements in the infinite set OA (N,2n,m), N ∈ ℕ. We discuss some examples which are explicitly solved with a software performing Hilbert bases computation.

AMS Subject Classification

62K15 13P10 


Orthogonal Array Integer Programming Hilbert Basis 


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Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  1. 1.Department of MathematicsPolitecnico di TorinoTurinItaly

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