New results on D-optimal Matrices

TL;DR

This paper introduces new D-optimal matrices of orders 206, 242, 262, and 482 by constructing supplementary difference sets with specific parameters, expanding the known set of such matrices.

Contribution

The paper presents the first construction of D-optimal matrices for four new orders through novel supplementary difference sets.

Findings

New D-optimal matrices of orders 206, 242, 262, 482 constructed.

Introduction of new supplementary difference sets with specific parameters.

Expansion of known D-optimal matrix orders.

Abstract

We construct a number of new (v;r,s;lambda) supplementary difference sets (SDS) with v odd and lambda = (r+s)-(v-1)/2. In particular, these give rise to D-optimal matrices of the four new orders 206, 242, 262, 482 constructed here for the first time.