On symmetric nets and generalized Hadamard matrices from affine designs |
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Authors: | Vassili C Mavron Vladimir D Tonchev |
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Institution: | (1) Department of Mathematics, The University of Wales, SY23 3BZ Aberystwyth, UK;(2) Department of Mathematical Sciences, Michigan Technological University, 49931 Houghton, Michigan, USA |
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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. |
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