MinT - Information on Result #599819

Information on Result #599819

There is no digital (6, 48, 58)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8⁴⁸, 58, F₈, 42) (dual of [58, 10, 43]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(8⁴⁷, 50, F₈, 42) (dual of [50, 3, 43]-code), but
  - â€œHi4â€ bound on codes from Brouwerâ€™s database [i]
2. OA(8¹⁰, 58, S₈, 8), but
  - discarding factors would yield OA(8¹⁰, 57, S₈, 8), but
    - the linear programming bound shows that MÂ â‰¥ 1426 626655 027200 / 1 315507 > 8¹⁰ [i]

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		Method
1	No digital (6, 49, 58)-net over F₈	[i]	m-Reduction
2	No digital (6, 50, 58)-net over F₈	[i]
3	No digital (6, 51, 58)-net over F₈	[i]
4	No digital (6, 52, 58)-net over F₈	[i]
5	No digital (6, 53, 58)-net over F₈	[i]
6	No digital (6, 54, 58)-net over F₈	[i]
7	No digital (6, 55, 58)-net over F₈	[i]
8	No digital (6, 56, 58)-net over F₈	[i]
9	No digital (6, 57, 58)-net over F₈	[i]
10	No digital (6, 58, 58)-net over F₈	[i]
11	No digital (6, 59, 58)-net over F₈	[i]
12	No digital (6, 60, 58)-net over F₈	[i]
13	No digital (6, 61, 58)-net over F₈	[i]
14	No digital (6, 62, 58)-net over F₈	[i]
15	No digital (6, 63, 58)-net over F₈	[i]
16	No digital (6, 64, 58)-net over F₈	[i]
17	No digital (6, 65, 58)-net over F₈	[i]
18	No digital (6, 66, 58)-net over F₈	[i]
19	No digital (6, 67, 58)-net over F₈	[i]
20	No digital (6, 68, 58)-net over F₈	[i]
21	No digital (6, 69, 58)-net over F₈	[i]
22	No digital (6, 70, 58)-net over F₈	[i]
23	No digital (6, 71, 58)-net over F₈	[i]
24	No digital (6, 72, 58)-net over F₈	[i]
25	No digital (6, 73, 58)-net over F₈	[i]
26	No digital (6, 74, 58)-net over F₈	[i]
27	No digital (6, 75, 58)-net over F₈	[i]
28	No digital (6, 76, 58)-net over F₈	[i]
29	No digital (6, 77, 58)-net over F₈	[i]
30	No digital (6, 78, 58)-net over F₈	[i]
31	No digital (6, 79, 58)-net over F₈	[i]
32	No digital (6, 80, 58)-net over F₈	[i]
33	No digital (6, 81, 58)-net over F₈	[i]
34	No digital (6, 82, 58)-net over F₈	[i]
35	No digital (6, 83, 58)-net over F₈	[i]
36	No digital (6, 84, 58)-net over F₈	[i]
37	No digital (6, 85, 58)-net over F₈	[i]
38	No digital (6, 86, 58)-net over F₈	[i]
39	No digital (6, 87, 58)-net over F₈	[i]
40	No digital (6, 88, 58)-net over F₈	[i]
41	No digital (6, 89, 58)-net over F₈	[i]
42	No digital (6, 90, 58)-net over F₈	[i]
43	No digital (6, 91, 58)-net over F₈	[i]
44	No digital (6, 92, 58)-net over F₈	[i]
45	No digital (6, 93, 58)-net over F₈	[i]
46	No digital (6, 94, 58)-net over F₈	[i]
47	No digital (6, 95, 58)-net over F₈	[i]
48	No digital (6, 96, 58)-net over F₈	[i]
49	No digital (6, 97, 58)-net over F₈	[i]
50	No digital (6, 98, 58)-net over F₈	[i]
51	No digital (6, 99, 58)-net over F₈	[i]
52	No digital (6, 100, 58)-net over F₈	[i]
53	No digital (6, 101, 58)-net over F₈	[i]
54	No digital (6, 102, 58)-net over F₈	[i]
55	No digital (6, 103, 58)-net over F₈	[i]
56	No digital (6, 104, 58)-net over F₈	[i]
57	No digital (6, 105, 58)-net over F₈	[i]
58	No digital (6, 106, 58)-net over F₈	[i]
59	No digital (6, 107, 58)-net over F₈	[i]
60	No digital (6, 108, 58)-net over F₈	[i]
61	No digital (6, 109, 58)-net over F₈	[i]
62	No digital (6, 110, 58)-net over F₈	[i]
63	No digital (6, 111, 58)-net over F₈	[i]
64	No digital (6, 112, 58)-net over F₈	[i]
65	No digital (6, 113, 58)-net over F₈	[i]
66	No digital (6, 114, 58)-net over F₈	[i]
67	No digital (6, 115, 58)-net over F₈	[i]
68	No digital (6, 116, 58)-net over F₈	[i]
69	No digital (6, 117, 58)-net over F₈	[i]
70	No digital (6, 118, 58)-net over F₈	[i]
71	No digital (6, 119, 58)-net over F₈	[i]
72	No digital (6, 120, 58)-net over F₈	[i]
73	No digital (6, 121, 58)-net over F₈	[i]
74	No digital (6, 122, 58)-net over F₈	[i]
75	No digital (6, 123, 58)-net over F₈	[i]
76	No digital (6, 124, 58)-net over F₈	[i]
77	No digital (6, 125, 58)-net over F₈	[i]
78	No digital (6, 126, 58)-net over F₈	[i]
79	No digital (6, 127, 58)-net over F₈	[i]
80	No digital (6, 128, 58)-net over F₈	[i]
81	No digital (6, 129, 58)-net over F₈	[i]
82	No digital (6, 130, 58)-net over F₈	[i]
83	No digital (6, 131, 58)-net over F₈	[i]
84	No digital (6, 132, 58)-net over F₈	[i]
85	No digital (6, 133, 58)-net over F₈	[i]
86	No digital (6, 134, 58)-net over F₈	[i]
87	No digital (6, 135, 58)-net over F₈	[i]
88	No digital (6, 136, 58)-net over F₈	[i]
89	No digital (6, 137, 58)-net over F₈	[i]
90	No digital (6, 138, 58)-net over F₈	[i]
91	No digital (6, 139, 58)-net over F₈	[i]
92	No digital (6, 140, 58)-net over F₈	[i]
93	No digital (6, 141, 58)-net over F₈	[i]
94	No digital (6, 142, 58)-net over F₈	[i]
95	No digital (6, 143, 58)-net over F₈	[i]
96	No digital (6, 144, 58)-net over F₈	[i]
97	No digital (6, 145, 58)-net over F₈	[i]
98	No digital (6, 146, 58)-net over F₈	[i]
99	No digital (6, 147, 58)-net over F₈	[i]
100	No digital (6, 148, 58)-net over F₈	[i]
101	No digital (6, 149, 58)-net over F₈	[i]
102	No digital (6, 150, 58)-net over F₈	[i]
103	No digital (6, 151, 58)-net over F₈	[i]
104	No digital (6, 152, 58)-net over F₈	[i]
105	No digital (6, 153, 58)-net over F₈	[i]
106	No digital (6, 154, 58)-net over F₈	[i]
107	No digital (6, 155, 58)-net over F₈	[i]
108	No digital (6, 156, 58)-net over F₈	[i]
109	No digital (6, 157, 58)-net over F₈	[i]
110	No digital (6, 158, 58)-net over F₈	[i]
111	No digital (6, 159, 58)-net over F₈	[i]
112	No digital (6, 160, 58)-net over F₈	[i]
113	No digital (6, 161, 58)-net over F₈	[i]
114	No digital (6, 162, 58)-net over F₈	[i]
115	No digital (6, 163, 58)-net over F₈	[i]
116	No digital (6, 164, 58)-net over F₈	[i]
117	No digital (6, 165, 58)-net over F₈	[i]
118	No digital (6, 166, 58)-net over F₈	[i]
119	No digital (6, 167, 58)-net over F₈	[i]
120	No digital (6, 168, 58)-net over F₈	[i]
121	No digital (6, 169, 58)-net over F₈	[i]
122	No digital (6, 170, 58)-net over F₈	[i]
123	No digital (6, 171, 58)-net over F₈	[i]
124	No digital (6, 172, 58)-net over F₈	[i]
125	No digital (6, 173, 58)-net over F₈	[i]
126	No digital (6, m, 58)-net over F₈ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net