89×89 {-1, +1} matrix of largest known determinant

Ratio of |Det R| to Barba bound: 0.751646

M=R^TR:

M=R R^T:

R:

Notes:

1. At this time the authors of this page do not have a matrix that achieves the stated determinant.
2. Cannot achieve Barba bound as 177=2×89-1 is not a perfect square.
3. This value was obtained by Farmakis and Kounias [FK] using an 88×88 Hadamard matrix of largest known excess. (The largest known excess is 792. The maximal excess is not known [FK].)