Technical note Open Access

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.

Files (298.0 kB)
Name Size
298.0 kB Download
  • Dragomir Ž Ðoković. Supplementary difference sets with symmetry for Hadamard matrices. Operators and Matrices, 3(4):557–569, 2009.

  • 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.

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

  • JM Goethals and JJ Seidel. A skew Hadamard matrix of order 36. Journal of the Australian Mathematical Society, 11(3):343–344, 1970.

  • Christos Koukouvinos and Stella Stylianou. On skew-Hadamard matrices. Discrete Mathematics, 308(13):2723–2731, 2008.

All versions This version
Views 350349
Downloads 8989
Data volume 26.5 MB26.5 MB
Unique views 338337
Unique downloads 8484


Cite as