MinT - Information on Result #599816

Information on Result #599816

There is no digital (5, 45, 50)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8⁴⁵, 50, F₈, 40) (dual of [50, 5, 41]-code), but

constructionÂ Y1 [i] would yield
1. OA(8⁴⁴, 46, S₈, 40), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 261336 857795 280739 939871 698507 597986 398208 / 41 > 8⁴⁴ [i]
2. OA(8⁵, 50, S₈, 4), but
  - discarding factors would yield OA(8⁵, 37, S₈, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 32894 > 8⁵ [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 (5, 46, 50)-net over F₈	[i]	m-Reduction
2	No digital (5, 47, 50)-net over F₈	[i]
3	No digital (5, 48, 50)-net over F₈	[i]
4	No digital (5, 49, 50)-net over F₈	[i]
5	No digital (5, 50, 50)-net over F₈	[i]
6	No digital (5, 51, 50)-net over F₈	[i]
7	No digital (5, 52, 50)-net over F₈	[i]
8	No digital (5, 53, 50)-net over F₈	[i]
9	No digital (5, 54, 50)-net over F₈	[i]
10	No digital (5, 55, 50)-net over F₈	[i]
11	No digital (5, 56, 50)-net over F₈	[i]
12	No digital (5, 57, 50)-net over F₈	[i]
13	No digital (5, 58, 50)-net over F₈	[i]
14	No digital (5, 59, 50)-net over F₈	[i]
15	No digital (5, 60, 50)-net over F₈	[i]
16	No digital (5, 61, 50)-net over F₈	[i]
17	No digital (5, 62, 50)-net over F₈	[i]
18	No digital (5, 63, 50)-net over F₈	[i]
19	No digital (5, 64, 50)-net over F₈	[i]
20	No digital (5, 65, 50)-net over F₈	[i]
21	No digital (5, 66, 50)-net over F₈	[i]
22	No digital (5, 67, 50)-net over F₈	[i]
23	No digital (5, 68, 50)-net over F₈	[i]
24	No digital (5, 69, 50)-net over F₈	[i]
25	No digital (5, 70, 50)-net over F₈	[i]
26	No digital (5, 71, 50)-net over F₈	[i]
27	No digital (5, 72, 50)-net over F₈	[i]
28	No digital (5, 73, 50)-net over F₈	[i]
29	No digital (5, 74, 50)-net over F₈	[i]
30	No digital (5, 75, 50)-net over F₈	[i]
31	No digital (5, 76, 50)-net over F₈	[i]
32	No digital (5, 77, 50)-net over F₈	[i]
33	No digital (5, 78, 50)-net over F₈	[i]
34	No digital (5, 79, 50)-net over F₈	[i]
35	No digital (5, 80, 50)-net over F₈	[i]
36	No digital (5, 81, 50)-net over F₈	[i]
37	No digital (5, 82, 50)-net over F₈	[i]
38	No digital (5, 83, 50)-net over F₈	[i]
39	No digital (5, 84, 50)-net over F₈	[i]
40	No digital (5, 85, 50)-net over F₈	[i]
41	No digital (5, 86, 50)-net over F₈	[i]
42	No digital (5, 87, 50)-net over F₈	[i]
43	No digital (5, 88, 50)-net over F₈	[i]
44	No digital (5, 89, 50)-net over F₈	[i]
45	No digital (5, 90, 50)-net over F₈	[i]
46	No digital (5, 91, 50)-net over F₈	[i]
47	No digital (5, 92, 50)-net over F₈	[i]
48	No digital (5, 93, 50)-net over F₈	[i]
49	No digital (5, 94, 50)-net over F₈	[i]
50	No digital (5, 95, 50)-net over F₈	[i]
51	No digital (5, 96, 50)-net over F₈	[i]
52	No digital (5, 97, 50)-net over F₈	[i]
53	No digital (5, 98, 50)-net over F₈	[i]
54	No digital (5, 99, 50)-net over F₈	[i]
55	No digital (5, 100, 50)-net over F₈	[i]
56	No digital (5, 101, 50)-net over F₈	[i]
57	No digital (5, 102, 50)-net over F₈	[i]
58	No digital (5, 103, 50)-net over F₈	[i]
59	No digital (5, 104, 50)-net over F₈	[i]
60	No digital (5, 105, 50)-net over F₈	[i]
61	No digital (5, 106, 50)-net over F₈	[i]
62	No digital (5, 107, 50)-net over F₈	[i]
63	No digital (5, 108, 50)-net over F₈	[i]
64	No digital (5, 109, 50)-net over F₈	[i]
65	No digital (5, 110, 50)-net over F₈	[i]
66	No digital (5, 111, 50)-net over F₈	[i]
67	No digital (5, 112, 50)-net over F₈	[i]
68	No digital (5, 113, 50)-net over F₈	[i]
69	No digital (5, 114, 50)-net over F₈	[i]
70	No digital (5, 115, 50)-net over F₈	[i]
71	No digital (5, 116, 50)-net over F₈	[i]
72	No digital (5, 117, 50)-net over F₈	[i]
73	No digital (5, 118, 50)-net over F₈	[i]
74	No digital (5, 119, 50)-net over F₈	[i]
75	No digital (5, 120, 50)-net over F₈	[i]
76	No digital (5, 121, 50)-net over F₈	[i]
77	No digital (5, 122, 50)-net over F₈	[i]
78	No digital (5, 123, 50)-net over F₈	[i]
79	No digital (5, 124, 50)-net over F₈	[i]
80	No digital (5, 125, 50)-net over F₈	[i]
81	No digital (5, 126, 50)-net over F₈	[i]
82	No digital (5, 127, 50)-net over F₈	[i]
83	No digital (5, 128, 50)-net over F₈	[i]
84	No digital (5, 129, 50)-net over F₈	[i]
85	No digital (5, 130, 50)-net over F₈	[i]
86	No digital (5, 131, 50)-net over F₈	[i]
87	No digital (5, 132, 50)-net over F₈	[i]
88	No digital (5, 133, 50)-net over F₈	[i]
89	No digital (5, 134, 50)-net over F₈	[i]
90	No digital (5, 135, 50)-net over F₈	[i]
91	No digital (5, 136, 50)-net over F₈	[i]
92	No digital (5, 137, 50)-net over F₈	[i]
93	No digital (5, 138, 50)-net over F₈	[i]
94	No digital (5, 139, 50)-net over F₈	[i]
95	No digital (5, 140, 50)-net over F₈	[i]
96	No digital (5, 141, 50)-net over F₈	[i]
97	No digital (5, 142, 50)-net over F₈	[i]
98	No digital (5, 143, 50)-net over F₈	[i]
99	No digital (5, 144, 50)-net over F₈	[i]
100	No digital (5, 145, 50)-net over F₈	[i]
101	No digital (5, 146, 50)-net over F₈	[i]
102	No digital (5, 147, 50)-net over F₈	[i]
103	No digital (5, 148, 50)-net over F₈	[i]
104	No digital (5, 149, 50)-net over F₈	[i]
105	No digital (5, 150, 50)-net over F₈	[i]
106	No digital (5, 151, 50)-net over F₈	[i]
107	No digital (5, 152, 50)-net over F₈	[i]
108	No digital (5, 153, 50)-net over F₈	[i]
109	No digital (5, 154, 50)-net over F₈	[i]
110	No digital (5, 155, 50)-net over F₈	[i]
111	No digital (5, 156, 50)-net over F₈	[i]
112	No digital (5, 157, 50)-net over F₈	[i]
113	No digital (5, 158, 50)-net over F₈	[i]
114	No digital (5, 159, 50)-net over F₈	[i]
115	No digital (5, 160, 50)-net over F₈	[i]
116	No digital (5, 161, 50)-net over F₈	[i]
117	No digital (5, 162, 50)-net over F₈	[i]
118	No digital (5, 163, 50)-net over F₈	[i]
119	No digital (5, 164, 50)-net over F₈	[i]
120	No digital (5, 165, 50)-net over F₈	[i]
121	No digital (5, 166, 50)-net over F₈	[i]
122	No digital (5, 167, 50)-net over F₈	[i]
123	No digital (5, 168, 50)-net over F₈	[i]
124	No digital (5, 169, 50)-net over F₈	[i]
125	No digital (5, 170, 50)-net over F₈	[i]
126	No digital (5, 171, 50)-net over F₈	[i]
127	No digital (5, 172, 50)-net over F₈	[i]
128	No digital (5, 173, 50)-net over F₈	[i]
129	No digital (5, m, 50)-net over F₈ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net