Undecided cases for D-optimal Designs of order
n º 0 mod 4
(Hadamard matrices)
Hadamard matrices
The
undecided cases for n < 2000 are 668, 716, 892, 1004, 1132, 1244, 1388,
1436, 1676, 1772, 1916, 1948, 1964.
Inequivalent Hadamard
matrices
In the
following Table, we give the known number Nn of inequivalent Hadamard
matrices of order n.
n
|
1
|
2
|
4
|
8
|
12
|
16
|
20
|
24
|
28
|
32
|
36
|
40
|
44
|
48
|
52
|
Nn
|
1
|
1
|
1
|
1
|
1
|
5
|
3
|
60
|
487
|
3578006
|
4745357
|
3.66x1011
|
500
|
3013006
|
638
|
n
|
56
|
60
|
64
|
68
|
72
|
76
|
80
|
84
|
88
|
92
|
96
|
100
|
Nn
|
2216264
|
256
|
1696940
|
340
|
1339890
|
10
|
4025308
|
13
|
3196189
|
12
|
1508441
|
17
|
For
orders 4, 8, 12, 16, 20, 24, 28 the above Table gives the exact numbers of
inequivalent Hadamard matrices. For orders >=32 the exact numbers are not known, but we present
here the known lower bounds.
Skew-Hadamard matrices
The
undecided cases for n < 1000 are 276, 356, 404, 428, 476, 596, 612, 668,
708, 712, 716, 764, 772, 804, 808, 820, 836, 852, 856, 872, 892, 900, 916, 932,
940, 952, 956, 980, 996.
Inequivalent skew-Hadamard
matrices
In the
following Table we give the known number SNn of inequivalent
skew-Hadamard matrices of order n.
|
n |
1 |
2 |
4 |
8 |
12 |
16 |
20 |
24 |
28 |
32 |
36 |
40 |
44 |
48 |
52 |
56 |
|
SNn |
1 |
1 |
1 |
1 |
1 |
2 |
1 |
16 |
54 |
6 |
18 |
22 |
59 |
1 |
561 |
1 |
For
orders 4, 8, 12, 16, 20, 24, 28 the above Table gives the exact numbers of
inequivalent skew-Hadamard matrices. For orders >=32 the exact numbers are not known, but we
present here the known lower bounds.
|
|
|
