Previous 33×33 {-1, +1} matrix of largest known determinant

Ratio of |Det R| to Barba bound: 0.790721

M=R^TR=R R^T:

33  9  1  1  1  1  1  1  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5
 9 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 1  1  1  1  1  1  1 33  1  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 33  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 33  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 33  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  1 33  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  1  1 33  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  1  1  1 33  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  1  1  1  1 33  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  1  1  1  1  1 33  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  1  1  1  1  1  1 33  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  1  1  1  1  1  1  1 33  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  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1  1
 5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1  1
 5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1  1
 5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1  1
 5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1  1
 5  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 33  1  1  1  1  1  1  1  1
 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 33  1  1  1  1  1  1  1
 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 33  1  1  1  1  1  1
 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 33  1  1  1  1  1
 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 33  1  1  1  1
 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 33  1  1  1
 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 33  1  1
 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 33  1
 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  1 33

R:

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

Notes:

1. This record has been supplanted by the matrix given here.
2. Cannot achieve Barba bound as 65=2×33-1 is not a perfect square.
3. This lower bound on the maximal determinant is obtained by applying the construction of Farmakis and Kounias [FK] to a 32×32 Hadamard matrix of maximal excess. Such a matrix was given by Enomoto and Miyamoto who proved the maximal excess to be 172 [EM].