Title

On symmetric nets and generalized Hadamard matrices from affine designs

Authors

Vassili C. Mavron, The University of Wales Aberystwyth
Vladimir Tonchev, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

3-2000

Abstract

Symmetric nets are affine resolvable designs whose duals are also affine. It is shown that. up to isomorphism, there are exactly four symmetric (3, 3)-nets (v=b=27,k=9), and exactly two inequivalent 9×9 generalized Hadamard matrices over the group of order 3. The symmetric (3, 3)-nets are found as subnets of affine resolvable 2-(27, 9, 4) designs. Ten of the 68 non-isomorphic affine resolvable 2-(27, 9, 4) designs are not extensions of symmetric (3, 3)-subnets, providing the first examples of affine 2-(q³, q², q²−1/q−1) designs without symmetric (q, q)-subnets.

Publisher's Statement

© Birkhäuser Verlag 2000. Publisher’s version of record: https://doi.org/10.1007/BF01220309

Publication Title

Journal of Geometry

Recommended Citation

Mavron, V. C., & Tonchev, V. (2000). On symmetric nets and generalized Hadamard matrices from affine designs. Journal of Geometry, 67(1-2), 180-187. http://doi.org/10.1007/BF01220309
Retrieved from: https://digitalcommons.mtu.edu/math-fp/139