84×84 {-1, +1} matrices of maximal determinant

|Det Rj| = 68271646134824810522683024903132926653619493012565170482×283 = 42×2141×283

Ratio of |Det Rj| to Hadamard bound: 1

M=RjTRj= Rj RjT=84 I
where I is the 84×84 identity matrix.


  1. Maximal matrix first reported by Paley [P].
  2. N. J. A. Sloane's Library of Hadamard matrices has three Hadamard matrices of order 84. Jennifer Seberry's web site lists seven Williamson-type Hadamard matrices of order 84.

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Page created 26 January 2003.
Last modified 26 January 2003.
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