论文信息 - Supplementary difference sets and D-optimal designs for n == 2 mod 4

Supplementary difference sets and D-optimal designs for n == 2 mod 4

Supplementary difference sets 2{12n; k, r; λ} are used to construct D-optimal designs for n ≡ 2 mod 4, where k, r, λ are defined through n. A number of new designs is constructed. The D-optimal design for n ≡ 86 is constructed for the first time. For n ≡ 2 mod 4, n<100 and for the cases n = 22, 34, 58, 70, 74, 78, 90, 94, 98, the D-optimal designs still remain unknown.

Th Chadjipantelis | Stratis Kounias

[1] L. D. Baumert. Cyclic Difference Sets , 1971 .

[2] Jennifer Seberry. On supplementary difference sets , 1972 .

[3] C. H. Yang. On designs of maximal (+1,-1)-matrices of order ≡2(\4). II , 1968 .

[4] C. H. Yang. A construction for maximal $\left( { + 1, - 1} \right)$-matrix of order $54$ , 1966 .

[5] Stratis Kounias,et al. Construction of D-Optimal Designs for N = 2 mod 4 Using Block-Circulant Matrices , 1985, J. Comb. Theory, Ser. A.

[6] C. H. Yang. Some designs for maximal (+1,-1)-determinant of order ≡2(4) , 1966 .

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

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

[9] C. H. Yang. On Designs of Maximal (+1, -1)-Matrices of Order n ≡2 (mod 4). II , 1968 .

[10] Jennifer Wallis,et al. On supplementary difference sets , 1972 .