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SBIBD(4k 2, 2k 2 +k,k 2 +k) and Hadamard matrices of order 4k 2 with maximal excess are equivalent

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Abstract

We show that anSBIBD(4k 2, 2k 2 +k,k 2 +k) is equivalent to a regular Hadamard matrix of order 4k 2 which is equivalent to an Hadamard matrix of order 4k 2 with maximal excess.

We find many newSBIBD(4k 2, 2k 2 +k,k 2 +k) including those for evenk when there is an Hadamard matrix of order 2k (in particular all 2k ≤ 210) andk ∈ {1, 3, 5,..., 29, 33,..., 41, 45, 51, 53, 61,..., 69, 75, 81, 83, 89, 95, 99, 625, 32m, 25⋅32m,m ≥ 0}.

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  1. Department of Computer Science, University College, The University of New South Wales, Australian Defence Force Academy, 2600, Canberra, ACT, Australia

    Jennifer Seberry

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  1. Jennifer Seberry
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Seberry, J. SBIBD(4k 2, 2k 2 +k,k 2 +k) and Hadamard matrices of order 4k 2 with maximal excess are equivalent. Graphs and Combinatorics 5, 373–383 (1989). https://doi.org/10.1007/BF01788694

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  • DOI: https://doi.org/10.1007/BF01788694

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