27×27 {-1, +1} matrices of largest known determinant

Ratio of |Det R_j| to Ehlich bound: 0.967268

M=R_j^TR_j=R_j R_j^T:

 27  3  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3 27  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3  3 27  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3  3  3 27  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3  3  3  3 27  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3  3  3  3  3 27  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
  3  3  3  3  3  3 27 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 27  3  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1  3 27  3  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1  3  3 27  3  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1  3  3  3 27  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1  3  3  3  3 27  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3 27  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3  3 27 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 27  3  3  3  3  3  3 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 27  3  3  3  3  3 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 27  3  3  3  3 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 27  3  3  3 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3 27  3  3 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3 27  3 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3  3 27 -1 -1 -1 -1 -1 -1 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 27  3  3  3  3  3 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 27  3  3  3  3 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 27  3  3  3 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 27  3  3 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3 27  3 
 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3  3  3 27 

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+--+--++--+-+-+--++--++++++
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-+-+-+--+-++---+-+--+++++++
-++---+-++--+--++-+--++++++

Notes:

1. This determinant surpasses a previous record. It was discovered by Hiroki Tamura and reported to this site on 26 August 2005.
2. Ehlich bound is not achievable as it is not an integer.
3. The matrix R₁ is not self dual. 66 inequivalent matrices can be obtained by the operations of transposition and switching (described in [O3]).
4. This form has not been proved optimal.