# 46×46 {-1, +1} matrices of maximal determinant

|Det Rj| = 3663123722407789250099445×245 = 495×1121×245 for j=1, 2 , ..., 17

Ratio of |Det Rj| to Ehlich/Wojtas bound: 1

M=RjTRj= Rj RjT for j=1, 2 , ..., 17:

```    | S   0 |
M = |       |
| 0   S |
```
with S = 44 I + 2 J where I is the 23×23 identity matrix and J is the 23×23 matrix with all entries 1.

There are 17 inequivalent matrices composed of circulant blocks, A and B:

``` | A   B |
|       |
|  T   T|
|-B   A |
```
The first rows of A and B are:
R1:
```+++++++-++-+++---+-++-+      +++---+--++++-+-+-++--+
```
R2:
```+++++++-+++-+++--+--+-+      +++--+-+-++++--++-+---+
```
R3:
```++++++++-+++-+-++-+---+      +++-+--++---+++-++--+-+
```
R4:
```++++++++-+---+++-+-++-+      +++-++--++-+--+++---+-+
```
R5:
```++++++++--+-+-+-++-++-+      +++---+++-++-+++---+--+
```
R6:
```++++++++-++-+-+-+-++--+      +++--+---++++---++-++-+
```
R7:
```++++++++-++---++++-+--+      +++-++-++---+-+-+-++--+
```
R8:
```+++++++++-+-+-++-++---+      ++-++----+++--++-++-+-+
```
R9:
```+++++++++---+-++-+++--+      ++-++---++-+--+-+++-+-+
```
R10:
```+++++++++-++--+-+++---+      ++-++---+++-+-+--+-++-+
```
R11:
```+++++++++---++-+++--+-+      +++--+-+--++--+-+++-+-+
```
R12:
```+++++++++--+-+-+++-+--+      +++-++-+-+++--+--++---+
```
R13:
```+++++++++-+---+-++++--+      +++--+-++-+-+-++--++--+
```
R14:
```+++++++++---+++-++--+-+      +++-++--+-++---++-+-+-+
```
R15:
```++++++++++---+-+++-+--+      ++-+-++-+-++-++--++---+
```
R16:
```++++++++++--+-++-++---+      ++--++-+-+-++-+++-+---+
```
R17:
```++++++++++----+++-++--+      ++--++-+--++-+-++-+-+-+
```

Notes:

1. A maximal determinant was first reported by Yang [Y1].
2. The complete set of 17 inequivalent circulant block forms was found by by Kounias, Koukouvinos, Nikolaou and Kakos [KKNK1].
3. Are there other inequivalent matrices not in the form of circulant blocks?

Back to maximal determinant main page.