The D-optimal saturated designs of order 22 |
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Authors: | Vasilis Chasiotis Stratis Kounias Nikos Farmakis |
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Institution: | 1. Department of Mathematics, Aristotle University, 54124, Thessaloniki, Greece;2. Department of Mathematics, University of Athens, 15784, Zografou, Athens, Greece |
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Abstract: | This paper attempts to prove the D-optimality of the saturated designs X and X of order 22, already existing in the current literature. The corresponding non-equivalent information matrices M=(X)X and M=(X)X have the maximum determinant. Within the application of a specific procedure, all symmetric and positive definite matrices M of order 22 with determinant the square of an integer and det(M) are constructed. This procedure has indicated that there are 26 such non-equivalent matrices M, for 24 of which the non-existence of designs X such that XX =M is proved. The remaining two matrices M are the information matrices M and M. |
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Keywords: | Information matrices Maximum determinant Equivalent matrices |
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