A new class of (near)-Hadamard matrices constructed by general supplementary difference sets (GSDS)

Abstract

It is well-known that there are some connections between combinatorial design and experimental design. Designs constructed from Hadamard matrices possess good properties such as D-optimality. In block designs, difference sets play an important role. In this work, we give a new idea called general supplementary difference sets (GSDS). It is used to propose an unified construction method for Hadamard matrix when the run size is 4n and near-Hadamard matrix when the run size is 4t + 2. These Hadamard-type matrices possess high D-efficiencies. In 1964, Ehlich had proved that a D-optimal design of order 2n-2 exists only if 2n-2 is the sum of two squares. Even in a small range from 1 to 100, there are still 6 parameters 22, 34, 58, 70, 78 and 94, which do not exist D-optimal designs. In this paper, we use GSDS to construct these designs with at least 99.5% D-efficiency.?