15×15 {-1, +1} matrix of maximal determinant

Ratio of |Det R| to Ehlich bound: 0.970725

M=R^TR=R R^T:

15  3  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3 15  3 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
 3  3 15 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 15  3  3  3 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1  3 15  3  3 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1  3  3 15  3 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1  3  3  3 15 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 15  3  3  3 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3 15  3  3 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3  3 15  3 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1  3  3  3 15 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 15  3  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3 15  3  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3 15  3
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  3  3  3 15

R:

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

Notes:

1. Ehlich bound is not achievable as it is not an integer.
2. This determinant was independently found by Smith [Sm] and Cohn [C1,C4] who conjectured it to be maximal. A proof of optimality was given by Orrick [O1].
3. M has block form.
4. R is unique up to equivalence [O1].