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

## 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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