The designs given here require a prime power for the number of levels. This is more a test of the accuracy of my transcription than of the original tables. The resulting fields have been tested by the methods described in Appendix 2 of that paper and they passed. The Galois field arithmetic for the prime powers is based on tables published by Knuth and Alanen (1964) below. That is q = p^r where p is prime and r >= 1 is an integer. Because of this the number of levels q must be a prime power. The constructions used are based on published algorithms that exploit properties of Galois fields. The programs below provide some choices to pick from, hopefully without too much of a compromise. It is entirely possible that no array of strength t > 1 is compatible with these conditions. One may also have a maximum value of n in mind and a minimum value for the number q of distinct levels to investigate. The notation for such an array is OA( n, k, q, t ). There would be lambda "overstrikes" at each point of the grid. Geometrically, if one were to "plot" the submatrix with one plotting axis for each of the t columns and one point in t dimensional space for each row, the result would be a grid of q^t distinct points. This number is the index of the array, commonly denoted lambda. The array has strength t if, in every n by t submatrix, the q^t possible distinct rows, all appear the same number of times. for many helpful electronic discussions that lead to improvements in these programs.Īn orthogonal array A is a matrix of n rows, k columns with every element being one of q symbols 0.,q-1. I thank the Semiconductor Research Corporation and the National Science Foundation for supporting this work.
#Latin hypercube sampling script python code#
This code comes with no warranty of any kind. From: programs construct and manipulate orthogonal arrays.
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