Information on Result #599878
There is no digital (5, 50, 55)-net over F9, because extracting embedded orthogonal array would yield linear OA(950, 55, F9, 45) (dual of [55, 5, 46]-code), but
- construction Y1 [i] would yield
- OA(949, 51, S9, 45), but
- the (dual) Plotkin bound shows that M ≥ 1 546132 562196 033993 109383 389296 863818 106322 566003 / 23 > 949 [i]
- OA(95, 55, S9, 4), but
- discarding factors would yield OA(95, 44, S9, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 60897 > 95 [i]
- discarding factors would yield OA(95, 44, S9, 4), but
- OA(949, 51, S9, 45), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
Result | This result only | Method | ||
---|---|---|---|---|
1 | No digital (5, 51, 55)-net over F9 | [i] | m-Reduction | |
2 | No digital (5, 52, 55)-net over F9 | [i] | ||
3 | No digital (5, 53, 55)-net over F9 | [i] | ||
4 | No digital (5, 54, 55)-net over F9 | [i] | ||
5 | No digital (5, 55, 55)-net over F9 | [i] | ||
6 | No digital (5, 56, 55)-net over F9 | [i] | ||
7 | No digital (5, 57, 55)-net over F9 | [i] | ||
8 | No digital (5, 58, 55)-net over F9 | [i] | ||
9 | No digital (5, 59, 55)-net over F9 | [i] | ||
10 | No digital (5, 60, 55)-net over F9 | [i] | ||
11 | No digital (5, 61, 55)-net over F9 | [i] | ||
12 | No digital (5, 62, 55)-net over F9 | [i] | ||
13 | No digital (5, 63, 55)-net over F9 | [i] | ||
14 | No digital (5, 64, 55)-net over F9 | [i] | ||
15 | No digital (5, 65, 55)-net over F9 | [i] | ||
16 | No digital (5, 66, 55)-net over F9 | [i] | ||
17 | No digital (5, 67, 55)-net over F9 | [i] | ||
18 | No digital (5, 68, 55)-net over F9 | [i] | ||
19 | No digital (5, 69, 55)-net over F9 | [i] | ||
20 | No digital (5, 70, 55)-net over F9 | [i] | ||
21 | No digital (5, 71, 55)-net over F9 | [i] | ||
22 | No digital (5, 72, 55)-net over F9 | [i] | ||
23 | No digital (5, 73, 55)-net over F9 | [i] | ||
24 | No digital (5, 74, 55)-net over F9 | [i] | ||
25 | No digital (5, 75, 55)-net over F9 | [i] | ||
26 | No digital (5, 76, 55)-net over F9 | [i] | ||
27 | No digital (5, 77, 55)-net over F9 | [i] | ||
28 | No digital (5, 78, 55)-net over F9 | [i] | ||
29 | No digital (5, 79, 55)-net over F9 | [i] | ||
30 | No digital (5, 80, 55)-net over F9 | [i] | ||
31 | No digital (5, 81, 55)-net over F9 | [i] | ||
32 | No digital (5, 82, 55)-net over F9 | [i] | ||
33 | No digital (5, 83, 55)-net over F9 | [i] | ||
34 | No digital (5, 84, 55)-net over F9 | [i] | ||
35 | No digital (5, 85, 55)-net over F9 | [i] | ||
36 | No digital (5, 86, 55)-net over F9 | [i] | ||
37 | No digital (5, 87, 55)-net over F9 | [i] | ||
38 | No digital (5, 88, 55)-net over F9 | [i] | ||
39 | No digital (5, 89, 55)-net over F9 | [i] | ||
40 | No digital (5, 90, 55)-net over F9 | [i] | ||
41 | No digital (5, 91, 55)-net over F9 | [i] | ||
42 | No digital (5, 92, 55)-net over F9 | [i] | ||
43 | No digital (5, 93, 55)-net over F9 | [i] | ||
44 | No digital (5, 94, 55)-net over F9 | [i] | ||
45 | No digital (5, 95, 55)-net over F9 | [i] | ||
46 | No digital (5, 96, 55)-net over F9 | [i] | ||
47 | No digital (5, 97, 55)-net over F9 | [i] | ||
48 | No digital (5, 98, 55)-net over F9 | [i] | ||
49 | No digital (5, 99, 55)-net over F9 | [i] | ||
50 | No digital (5, 100, 55)-net over F9 | [i] | ||
51 | No digital (5, 101, 55)-net over F9 | [i] | ||
52 | No digital (5, 102, 55)-net over F9 | [i] | ||
53 | No digital (5, 103, 55)-net over F9 | [i] | ||
54 | No digital (5, 104, 55)-net over F9 | [i] | ||
55 | No digital (5, 105, 55)-net over F9 | [i] | ||
56 | No digital (5, 106, 55)-net over F9 | [i] | ||
57 | No digital (5, 107, 55)-net over F9 | [i] | ||
58 | No digital (5, 108, 55)-net over F9 | [i] | ||
59 | No digital (5, 109, 55)-net over F9 | [i] | ||
60 | No digital (5, 110, 55)-net over F9 | [i] | ||
61 | No digital (5, 111, 55)-net over F9 | [i] | ||
62 | No digital (5, 112, 55)-net over F9 | [i] | ||
63 | No digital (5, 113, 55)-net over F9 | [i] | ||
64 | No digital (5, 114, 55)-net over F9 | [i] | ||
65 | No digital (5, 115, 55)-net over F9 | [i] | ||
66 | No digital (5, 116, 55)-net over F9 | [i] | ||
67 | No digital (5, 117, 55)-net over F9 | [i] | ||
68 | No digital (5, 118, 55)-net over F9 | [i] | ||
69 | No digital (5, 119, 55)-net over F9 | [i] | ||
70 | No digital (5, 120, 55)-net over F9 | [i] | ||
71 | No digital (5, 121, 55)-net over F9 | [i] | ||
72 | No digital (5, 122, 55)-net over F9 | [i] | ||
73 | No digital (5, 123, 55)-net over F9 | [i] | ||
74 | No digital (5, 124, 55)-net over F9 | [i] | ||
75 | No digital (5, 125, 55)-net over F9 | [i] | ||
76 | No digital (5, 126, 55)-net over F9 | [i] | ||
77 | No digital (5, 127, 55)-net over F9 | [i] | ||
78 | No digital (5, 128, 55)-net over F9 | [i] | ||
79 | No digital (5, 129, 55)-net over F9 | [i] | ||
80 | No digital (5, 130, 55)-net over F9 | [i] | ||
81 | No digital (5, 131, 55)-net over F9 | [i] | ||
82 | No digital (5, 132, 55)-net over F9 | [i] | ||
83 | No digital (5, 133, 55)-net over F9 | [i] | ||
84 | No digital (5, 134, 55)-net over F9 | [i] | ||
85 | No digital (5, 135, 55)-net over F9 | [i] | ||
86 | No digital (5, 136, 55)-net over F9 | [i] | ||
87 | No digital (5, 137, 55)-net over F9 | [i] | ||
88 | No digital (5, 138, 55)-net over F9 | [i] | ||
89 | No digital (5, 139, 55)-net over F9 | [i] | ||
90 | No digital (5, 140, 55)-net over F9 | [i] | ||
91 | No digital (5, 141, 55)-net over F9 | [i] | ||
92 | No digital (5, 142, 55)-net over F9 | [i] | ||
93 | No digital (5, 143, 55)-net over F9 | [i] | ||
94 | No digital (5, 144, 55)-net over F9 | [i] | ||
95 | No digital (5, 145, 55)-net over F9 | [i] | ||
96 | No digital (5, 146, 55)-net over F9 | [i] | ||
97 | No digital (5, 147, 55)-net over F9 | [i] | ||
98 | No digital (5, 148, 55)-net over F9 | [i] | ||
99 | No digital (5, 149, 55)-net over F9 | [i] | ||
100 | No digital (5, 150, 55)-net over F9 | [i] | ||
101 | No digital (5, m, 55)-net over F9 for arbitrarily large m | [i] | m-Reduction from Arbitrarily Large Net |