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

|Det R| = 25515×214 = 105×35×214

Ratio of |Det R| to Ehlich bound: 0.970725

M=RTR=R RT:

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].

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Page created 26 January 2002.
Last modified 15 January 2004.
Comments: maxdet@indiana.edu