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D-Optimal Matrices of Orders 118, 138, 150, 154 and 174

  • Dragomir Ž.-Doković
  • Ilias S. Kotsireas
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 133)

Abstract

We construct supplementary difference sets (SDSs) with parameters (59; 28, 22; 21), (69; 31, 27; 24), (75; 36, 29; 28), (77; 34, 31; 27) and (87; 38, 36; 31). These SDSs give D-optimal designs (DO-designs) of two-circulant type of orders 118,138,150,154 and 174. Until now, no DO-designs of orders 138,154 and 174 were known. While a DO-design (not of two-circulant type) of order 150 was constructed previously by Holzmann and Kharaghani, no such design of two-circulant type was known. The smallest undecided order for DO-designs is now 198. We use a novel property of the compression map to speed up some computations.

Keywords

D-optimal designs Supplementary difference sets Periodic autocorrelation function Compression method 

Notes

Acknowledgements

The authors wish to acknowledge generous support by NSERC. This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET) and Compute/Calcul Canada. We thank a referee for his suggestions.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Physics & Computer ScienceWilfrid Laurier UniversityWaterlooCanada

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