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The Best Matrix Conjecture

Curtis Bright

This note describes the best matrix conjecture from combinatorial design theory and the latest results that are known on the conjecture.  In particular, examples of best matrices in orders \(r^2+r+1\) for all \(r\) up to and including 6 are given.

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  • Dragomir Ž Ðoković and Ilias S Kotsireas. Goethals–Seidel difference families with symmetric or skew base blocks. Mathematics in Computer Science, 12: 373–388, 2018.

  • Dragomir Ž Ðoković. Supplementary difference sets with symmetry for Hadamard matrices. Operators and Matrices, 3(4):557–569, 2009.

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  • S Georgiou, C Koukouvinos, and Jennifer Seberry. On circulant best matrices and their applications. Linear and Multilinear Algebra, 48(3):263–274, 2001.

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