论文信息 - A construction of d-optimal weighing designs when n3 mod 4

A construction of d-optimal weighing designs when n3 mod 4

Abstract A new method is given for constructing D-optimal weighing designs when n 3 mod 4. A matrix of the Goethals-Seidel type is employed and the circulant blocks consist of circular matrices. The new designs, so constructed for n n,k,s )=(23,15,11), (23,16,9), (35,23,11), (35,24,11), (39,23,17), (39,24,12), (39,24,13), (47,29,14), (47,29,15), (47,30,13), (55,31,23), (55,32,16), (55,32,17), (59,35,17), (59,36,16), (59,39,12), (59,40,11), (59,41,11), (71,39,29), (71,40,20), (71,40,21), (71,41,20), (71,41,21), (71,42,19), (83,47,24), (83,48,21), (87,47,35), (87,48,24), (87,48,25), (95,53,26), (95,53,27).

Stratis Kounias | Nikos Farmakis | S. Kounias | N. Farmakis

[1] Z. Galil,et al. $D$-Optimum Weighing Designs , 1980 .

[2] M. Wojtas,et al. On Hadamard's inequality for the determinants of order non-divisible by 4 , 1964 .

[3] A. Street,et al. Combinatorics: room squares, sum-free sets, Hadamard matrices , 1972 .

[4] H. Ehlich,et al. Determinantenabschätzungen für binäre Matrizen , 1964 .

[5] H. Ehlich,et al. Determinantenabschätzung für binäre Matrizen mitn≡3 mod 4 , 1964 .

[6] Z. Galil,et al. Construction Methods for D-Optimum Weighing Designs when n ≡ 3(mod 4) , 1985 .

[7] Stratis Kounias,et al. Some d-optimal weighing designs for n≡ (mod 4) , 1983 .

[8] S. Kounias,et al. The exact D-optimal first order saturated design with 17 observations , 1982 .

[9] Z. Galil,et al. Construction Methods for $D$-Optimum Weighing Designs when $n \equiv 3 (\operatorname{mod} 4)$ , 1982 .

[10] W. Wallis,et al. Hadamard Matrices and Their Applications , 1978 .