Hilbert Bases for Orthogonal Arrays
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Abstract
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 13P10Keywords
Orthogonal Array Integer Programming Hilbert BasisPreview
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