# Constructing near-Hadamard designs with (almost) D-optimality by general supplementary difference sets

@article{and2017ConstructingND, title={Constructing near-Hadamard designs with (almost) D-optimality by general supplementary difference sets}, author={Yuan-Lung Lin and and F. Phoa}, journal={Statistica Sinica}, year={2017} }

We propose a new and unified construction method, general supplementary difference sets (GSDS)s, for near-Hadamard designs when the run sizes are n ≡ 2 (mod 4). These designs possess high D-efficiencies. Ehlich (1964) derived an upper bound for the determinant of matrices of order n ≡ 2 (mod 4) achievable only if 2n − 2 is a sum of two squares. Between 1 to 100, there are 6 parameters, 22, 34, 58, 70, 78, and 94, that do not fulfill this condition. We formulate a class of near-Hadamard designs… Expand

#### One Citation

The D-optimal saturated designs of order 22

- Mathematics, Computer Science
- Discret. Math.
- 2018

The D-optimality of the saturated designs X ∗ and X∗ ∗ of order 22 is proved, for 24 of which the non-existence of designs X such that X T X =M is proved. Expand

#### References

SHOWING 1-10 OF 29 REFERENCES

Supplementary difference sets and optimal designs

- Computer Science, Mathematics
- Discret. Math.
- 1991

Abstract D-optimal designs of order n = 2 v ≡ 2 (mod 4), where q is a prime power and v = q2 + q + 1 are constructed using two methods, one with supplementary difference sets and the other using… Expand

Some new D-optimal designs

- Mathematics, Computer Science
- Australas. J Comb.
- 1997

Several new (v; r, 8; A) supplementary difference sets with v odd and T' + .5 = A + (v 1) /2.5 are constructed here for the first time, giving rise to D-optimal designs of order 2v. Expand

Heuristic algorithms for Hadamard matrices with two circulant cores

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2008

Heuristic algorithms to construct Hadamard matrices with two circulant cores based on local and tabu search and they use information on the geometry of the objective function landscapes to detect when solutions of a special structure exist. Expand

An experimental search and new combinatorial designs via a generalisation of cyclotomy

- Mathematics
- 1998

Cyclotomy can be used to construct a variety of combinatorial designs, for example, supplementary difference sets, weighing matrices and T -matrices. These designs may be obtained by using linear… Expand

Hadamard ideals and Hadamard matrices with two circulant cores

- Computer Science, Mathematics
- Eur. J. Comb.
- 2006

The concept of Hadamard ideal is introduced, to systematize the application of computational algebra methods to the construction of HadAmard matrices with two circulant cores, given by Fletcher, Gysin and Seberry. Expand

The maximal determinant of cocyclic (-1,1)-matrices over D2t

- Mathematics
- 2012

Abstract Cocyclic construction has been successfully used for Hadamard matrices of order n. These ( - 1 , 1 ) -matrices satisfy that HH T = H T H = nI and give the solution to the maximal determinant… Expand

New Results on D-Optimal Matrices

- Mathematics
- 2011

We construct a number of new supplementary difference sets (SDS) with v odd and . In particular, these give rise to D-optimal matrices of the four new orders 206, 242, 262, 482, constructed here for… Expand

Bounds on the maximum determinant for (1,-1) matrices

- Mathematics
- 2000

We suppose the Hadamard conjecture is true and an Hadamard matrix of order 4t, exists for all t ≥ 1. We use the results for the equivalent SBIBD(4t-1,2t-1,t-1) to establish the maximum determinant or… Expand

Recent developments in nonregular fractional factorial designs

- Mathematics, Computer Science
- 2008

Important developments in optimality criteria and comparison are reviewed, including projection properties, generalized resolution, various generalized minimum aberration criteria, optimality results, construction methods and analysis strategies for nonregular designs. Expand

A systematic approach for the construction of definitive screening designs

- Computer Science
- 2015

This paper investigates the structure of three-level DS designs and suggests a theoretically-driven approach to constructing DS designs for any number of run size, which is computationally efficient and universal to designs with even or odd number of factors. Expand