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Orthogonal Designs Of Kharaghani Type: Ii, C. Koukouvinos, Jennifer Seberry
Orthogonal Designs Of Kharaghani Type: Ii, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
H. Kharaghani, in "Arrays for orthogonal designs", J. Combin. Designs, 8 (2000), 166-173, showed how to use amicable sets of matrices to construct orthogonal designs in orders divisible by eight. We show how amicable orthogonal designs can be used to make amicable sets and so obtain infinite families of orthogonal designs in six variables in orders divisible by eight.
Orthogonal Designs Of Kharaghani Type: I, C. Koukouvinos, Jennifer Seberry
Orthogonal Designs Of Kharaghani Type: I, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We use an array given in H. Kharaghani, Arrays for orthogonal designs, J. Combin. Designs, 8 (2000), 166-173, to obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; hi, kl, kl, kl, k2, k2, k2, k2), where k1 and k2 must be the sum of two squares. In particular we obtain infinite families of 8-variable Kharaghani type orthogonal designs, OD(8t; k, k, k, k, k, k, k, k). For odd t orthogonal designs of order ≡ 8( mod 16) can have at most eight variables.