45×45 {-1, +1} matrix of largest known determinant

|Det R| = 658622245038976249007779×244 = 89×1121×244

Ratio of |Det R| to Barba bound: 0.857635

M=RTR:

 45  5  5  5  5  5  5  5  5  5  5  1  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1 
  5 45  1  1  1  1  1  1  1  1  1 -3  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1 
  5  1 45  1  1  1  1  1  1  1  1 -3  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1 
  5  1  1 45  1  1  1  1  1  1  1 -3  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1 
  5  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1 
  1 -3 -3 -3  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1 
  5  5  5  5  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1 
 -3 -3 -3 -3  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
  5  5  5  5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  1  1  1  1  1  1  1  1  1  1  1 
  5  5  5  5  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  1  1  1 45  1  1  1  1  1  1  1  1  1  1 
 -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  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45 

M'=R RT:

 45  5  5  5  9  5  5  5  5  5  1  1  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
  5 45  1  1  5  1  1  1  1  1 -3 -3  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
  5  1 45  1  5  1  1  1  1  1 -3 -3  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
  5  1  1 45  5  1  1  1  1  1 -3 -3  5 -3  1  1  1  1  1  1  1  1  1  5 -3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
  9  5  5  5 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1 
  5  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1 
  1 -3 -3 -3  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1 
  1 -3 -3 -3  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1 
  5  5  5  5  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1 
 -3 -3 -3 -3  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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 
  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 
  5  5  5  5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 45 

R:

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

Notes:

  1. This matrix was constructed in August 2009 by [BOOZ] from a doubly-three-normalized Hadamard matrix of size 44 and excess 220 by the method used in size 37 in [OS]. It surpasses a previous record.
  2. Cannot achieve Barba bound as 89=2×45-1 is not a perfect square.

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Page created 6 October 2012.
Last modified 6 October 2012.
Comments: maxdet@indiana.edu