Support Sets S_m & Exact Minimal Dyadic Blocks
Out[]//TableForm=
m
S_m
|S_m|
Max S_m
Absolute Minimal Blocks
1
{0, 1}
2
1
B(0, 1)
2
{1, 2}
2
2
B(1, 2) Δ B(2, 1)
3
{2, 3, 4}
3
4
B(2, 1) Δ B(4, 0)
4
{1, 2, 4, 6, 7}
5
7
B(0, 1) Δ B(0, 6) Δ B(7, 0)
5
{1, 6, 8}
3
8
B(1, 8) Δ B(6, 0) Δ B(8, 1)
6
{1, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16}
11
16
B(0, 7) Δ B(0, 10) Δ B(7, 0) Δ B(9, 0) Δ B(9, 6) Δ B(16, 0)
7
{1, 4, 7, 11, 13, 14, 15, 16, 18, 23, 25}
11
25
B(0, 10) Δ B(0, 19) Δ B(3, 20) Δ B(4, 8) Δ B(8, 7) Δ B(9, 0) Δ B(17, 8)
8
{1, 6, 8, 9, 10, 11, 13, 15, 16, 19, 20, 22, 23, 25, 26, 27, 30, 31, 32}
19
32
B(1, 8) Δ B(6, 16) Δ B(8, 7) Δ B(9, 16) Δ B(12, 2) Δ B(16, 6) Δ B(18, 13) Δ B(32, 0)
Truncated Support Sets S_m (k=8)
m
S_m
|S_m|
Max S_m
1
{0, 1}
2
1
2
{1, 2}
2
2
3
{2, 3, 4}
3
4
4
{1, 2, 4, 6, 7}
5
7
5
{1, 6, 8}
3
8
6
{1, 3, 4, 5, 6, 8, 10, 11, 13, 15, 16}
11
16
7
{1, 4, 7, 11, 13, 14, 15, 16, 18, 23, 25}
11
25
8
{1, 6, 8, 9, 10, 11, 13, 15, 16, 19, 20, 22, 23, 25, 26, 27, 30, 31, 32}
19
32
9
{1, 5, 6, 7, 13, 15, 21, 22, 24, 25, 26, 27, 30, 31, 34, 37, 40, 44, 46, 47, 48, 49, 51, 56, 58}
25
58
10
{1, 6, 8, 9, 10, 11, 12, 14, 16, 17, 18, 21, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 43, 44, 47, 48, 51, 52, 53, 55, 60, 62, 64}
33
64
11
{1, 14, 16, 20, 22, 25, 26, 27, 32, 35, 36, 38, 39, 41, 42, 44, 45, 46, 47, 50, 51, 54, 55, 59, 62, 64, 66, 70, 71, 72, 78, 80, 86, 87, 89, 90, 91, 92, 95, 96, 99, 102, 105, 109, 111, 112, 113, 114, 116, 121, 123}
51
123
12
{1, 7, 8, 9, 10, 11, 12, 13, 14, 18, 20, 21, 24, 25, 27, 31, 32, 34, 36, 38, 39, 41, 43, 45, 48, 49, 50, 51, 52, 53, 54, 55, 56, 62, 64, 67, 68, 73, 74, 80, 82, 84, 85, 88, 90, 92, 93, 94, 98, 100, 101, 104, 106, 107, 110, 111, 112, 113, 118, 119, 120, 124, 126}
63
126
13
{1, 8, 15, 17, 18, 19, 20, 21, 22, 24, 32, 35, 36, 40, 41, 42, 48, 49, 52, 53, 56, 57, 58, 62, 63, 64, 69, 70, 72, 75, 76, 77, 84, 85, 87, 88, 89, 90, 91, 94, 95, 96, 97, 98, 100, 103, 104, 106, 112, 113, 115, 118, 119, 121, 124, 125, 127}
57
127
14
{1, 10, 16, 18, 20, 26, 28, 40, 42, 46, 48, 50, 52, 54, 57, 59, 61, 62, 64, 68, 78, 82, 87, 88, 90, 95, 96, 100, 102, 104, 107, 108, 110, 111, 112, 114, 117, 118, 122, 123, 125, 127, 128}
43
128