D-optimal matrices of orders 118, 138, 150, 154 and 174

TL;DR

This paper constructs new D-optimal designs of specific orders using supplementary difference sets, including some orders where no such designs were previously known, and introduces a novel computational method.

Contribution

It presents the first known two-circulant D-optimal designs for orders 138, 154, and 174, and introduces a new property of the compression map to enhance computational efficiency.

Findings

Constructed SDSs for specified parameters.

Established new D-optimal designs of orders 138, 154, and 174.

Developed a novel property of the compression map for faster computations.

Abstract

We construct supplementary difference sets (SDS) 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.