MinT - Information on Result #599812

Information on Result #599812

There is no digital (4, 36, 41)-net over F₈, because extracting embedded orthogonal array would yield linear OA(8³⁶, 41, F₈, 32) (dual of [41, 5, 33]-code), but

constructionÂ Y1 [i] would yield
1. OA(8³⁵, 37, S₈, 32), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 1622 592768 292133 633915 780102 881280 / 33 > 8³⁵ [i]
2. OA(8⁵, 41, 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 (4, 37, 41)-net over F₈	[i]	m-Reduction
2	No digital (4, 38, 41)-net over F₈	[i]
3	No digital (4, 39, 41)-net over F₈	[i]
4	No digital (4, 40, 41)-net over F₈	[i]
5	No digital (4, 41, 41)-net over F₈	[i]
6	No digital (4, 42, 41)-net over F₈	[i]
7	No digital (4, 43, 41)-net over F₈	[i]
8	No digital (4, 44, 41)-net over F₈	[i]
9	No digital (4, 45, 41)-net over F₈	[i]
10	No digital (4, 46, 41)-net over F₈	[i]
11	No digital (4, 47, 41)-net over F₈	[i]
12	No digital (4, 48, 41)-net over F₈	[i]
13	No digital (4, 49, 41)-net over F₈	[i]
14	No digital (4, 50, 41)-net over F₈	[i]
15	No digital (4, 51, 41)-net over F₈	[i]
16	No digital (4, 52, 41)-net over F₈	[i]
17	No digital (4, 53, 41)-net over F₈	[i]
18	No digital (4, 54, 41)-net over F₈	[i]
19	No digital (4, 55, 41)-net over F₈	[i]
20	No digital (4, 56, 41)-net over F₈	[i]
21	No digital (4, 57, 41)-net over F₈	[i]
22	No digital (4, 58, 41)-net over F₈	[i]
23	No digital (4, 59, 41)-net over F₈	[i]
24	No digital (4, 60, 41)-net over F₈	[i]
25	No digital (4, 61, 41)-net over F₈	[i]
26	No digital (4, 62, 41)-net over F₈	[i]
27	No digital (4, 63, 41)-net over F₈	[i]
28	No digital (4, 64, 41)-net over F₈	[i]
29	No digital (4, 65, 41)-net over F₈	[i]
30	No digital (4, 66, 41)-net over F₈	[i]
31	No digital (4, 67, 41)-net over F₈	[i]
32	No digital (4, 68, 41)-net over F₈	[i]
33	No digital (4, 69, 41)-net over F₈	[i]
34	No digital (4, 70, 41)-net over F₈	[i]
35	No digital (4, 71, 41)-net over F₈	[i]
36	No digital (4, 72, 41)-net over F₈	[i]
37	No digital (4, 73, 41)-net over F₈	[i]
38	No digital (4, 74, 41)-net over F₈	[i]
39	No digital (4, 75, 41)-net over F₈	[i]
40	No digital (4, 76, 41)-net over F₈	[i]
41	No digital (4, 77, 41)-net over F₈	[i]
42	No digital (4, 78, 41)-net over F₈	[i]
43	No digital (4, 79, 41)-net over F₈	[i]
44	No digital (4, 80, 41)-net over F₈	[i]
45	No digital (4, 81, 41)-net over F₈	[i]
46	No digital (4, 82, 41)-net over F₈	[i]
47	No digital (4, 83, 41)-net over F₈	[i]
48	No digital (4, 84, 41)-net over F₈	[i]
49	No digital (4, 85, 41)-net over F₈	[i]
50	No digital (4, 86, 41)-net over F₈	[i]
51	No digital (4, 87, 41)-net over F₈	[i]
52	No digital (4, 88, 41)-net over F₈	[i]
53	No digital (4, 89, 41)-net over F₈	[i]
54	No digital (4, 90, 41)-net over F₈	[i]
55	No digital (4, 91, 41)-net over F₈	[i]
56	No digital (4, 92, 41)-net over F₈	[i]
57	No digital (4, 93, 41)-net over F₈	[i]
58	No digital (4, 94, 41)-net over F₈	[i]
59	No digital (4, 95, 41)-net over F₈	[i]
60	No digital (4, 96, 41)-net over F₈	[i]
61	No digital (4, 97, 41)-net over F₈	[i]
62	No digital (4, 98, 41)-net over F₈	[i]
63	No digital (4, 99, 41)-net over F₈	[i]
64	No digital (4, 100, 41)-net over F₈	[i]
65	No digital (4, 101, 41)-net over F₈	[i]
66	No digital (4, 102, 41)-net over F₈	[i]
67	No digital (4, 103, 41)-net over F₈	[i]
68	No digital (4, 104, 41)-net over F₈	[i]
69	No digital (4, 105, 41)-net over F₈	[i]
70	No digital (4, 106, 41)-net over F₈	[i]
71	No digital (4, 107, 41)-net over F₈	[i]
72	No digital (4, 108, 41)-net over F₈	[i]
73	No digital (4, 109, 41)-net over F₈	[i]
74	No digital (4, 110, 41)-net over F₈	[i]
75	No digital (4, 111, 41)-net over F₈	[i]
76	No digital (4, 112, 41)-net over F₈	[i]
77	No digital (4, 113, 41)-net over F₈	[i]
78	No digital (4, 114, 41)-net over F₈	[i]
79	No digital (4, 115, 41)-net over F₈	[i]
80	No digital (4, 116, 41)-net over F₈	[i]
81	No digital (4, 117, 41)-net over F₈	[i]
82	No digital (4, 118, 41)-net over F₈	[i]
83	No digital (4, 119, 41)-net over F₈	[i]
84	No digital (4, 120, 41)-net over F₈	[i]
85	No digital (4, 121, 41)-net over F₈	[i]
86	No digital (4, 122, 41)-net over F₈	[i]
87	No digital (4, 123, 41)-net over F₈	[i]
88	No digital (4, 124, 41)-net over F₈	[i]
89	No digital (4, 125, 41)-net over F₈	[i]
90	No digital (4, 126, 41)-net over F₈	[i]
91	No digital (4, 127, 41)-net over F₈	[i]
92	No digital (4, 128, 41)-net over F₈	[i]
93	No digital (4, 129, 41)-net over F₈	[i]
94	No digital (4, 130, 41)-net over F₈	[i]
95	No digital (4, 131, 41)-net over F₈	[i]
96	No digital (4, 132, 41)-net over F₈	[i]
97	No digital (4, 133, 41)-net over F₈	[i]
98	No digital (4, 134, 41)-net over F₈	[i]
99	No digital (4, 135, 41)-net over F₈	[i]
100	No digital (4, 136, 41)-net over F₈	[i]
101	No digital (4, 137, 41)-net over F₈	[i]
102	No digital (4, 138, 41)-net over F₈	[i]
103	No digital (4, 139, 41)-net over F₈	[i]
104	No digital (4, 140, 41)-net over F₈	[i]
105	No digital (4, 141, 41)-net over F₈	[i]
106	No digital (4, 142, 41)-net over F₈	[i]
107	No digital (4, 143, 41)-net over F₈	[i]
108	No digital (4, 144, 41)-net over F₈	[i]
109	No digital (4, 145, 41)-net over F₈	[i]
110	No digital (4, 146, 41)-net over F₈	[i]
111	No digital (4, 147, 41)-net over F₈	[i]
112	No digital (4, 148, 41)-net over F₈	[i]
113	No digital (4, 149, 41)-net over F₈	[i]
114	No digital (4, 150, 41)-net over F₈	[i]
115	No digital (4, 151, 41)-net over F₈	[i]
116	No digital (4, 152, 41)-net over F₈	[i]
117	No digital (4, 153, 41)-net over F₈	[i]
118	No digital (4, 154, 41)-net over F₈	[i]
119	No digital (4, 155, 41)-net over F₈	[i]
120	No digital (4, 156, 41)-net over F₈	[i]
121	No digital (4, 157, 41)-net over F₈	[i]
122	No digital (4, 158, 41)-net over F₈	[i]
123	No digital (4, 159, 41)-net over F₈	[i]
124	No digital (4, 160, 41)-net over F₈	[i]
125	No digital (4, 161, 41)-net over F₈	[i]
126	No digital (4, 162, 41)-net over F₈	[i]
127	No digital (4, 163, 41)-net over F₈	[i]
128	No digital (4, 164, 41)-net over F₈	[i]
129	No digital (4, 165, 41)-net over F₈	[i]
130	No digital (4, 166, 41)-net over F₈	[i]
131	No digital (4, 167, 41)-net over F₈	[i]
132	No digital (4, 168, 41)-net over F₈	[i]
133	No digital (4, 169, 41)-net over F₈	[i]
134	No digital (4, 170, 41)-net over F₈	[i]
135	No digital (4, 171, 41)-net over F₈	[i]
136	No digital (4, 172, 41)-net over F₈	[i]
137	No digital (4, 173, 41)-net over F₈	[i]
138	No digital (4, m, 41)-net over F₈ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net