MinT - Information on Result #599874

Information on Result #599874

There is no digital (4, 40, 45)-net over F₉, because extracting embedded orthogonal array would yield linear OA(9⁴⁰, 45, F₉, 36) (dual of [45, 5, 37]-code), but

constructionÂ Y1 [i] would yield
1. OA(9³⁹, 41, S₉, 36), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 739 044147 071729 616580 416051 031916 488005 / 37 > 9³⁹ [i]
2. OA(9⁵, 45, S₉, 4), but
  - discarding factors would yield OA(9⁵, 44, S₉, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 60897 > 9⁵ [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, 41, 45)-net over F₉	[i]	m-Reduction
2	No digital (4, 42, 45)-net over F₉	[i]
3	No digital (4, 43, 45)-net over F₉	[i]
4	No digital (4, 44, 45)-net over F₉	[i]
5	No digital (4, 45, 45)-net over F₉	[i]
6	No digital (4, 46, 45)-net over F₉	[i]
7	No digital (4, 47, 45)-net over F₉	[i]
8	No digital (4, 48, 45)-net over F₉	[i]
9	No digital (4, 49, 45)-net over F₉	[i]
10	No digital (4, 50, 45)-net over F₉	[i]
11	No digital (4, 51, 45)-net over F₉	[i]
12	No digital (4, 52, 45)-net over F₉	[i]
13	No digital (4, 53, 45)-net over F₉	[i]
14	No digital (4, 54, 45)-net over F₉	[i]
15	No digital (4, 55, 45)-net over F₉	[i]
16	No digital (4, 56, 45)-net over F₉	[i]
17	No digital (4, 57, 45)-net over F₉	[i]
18	No digital (4, 58, 45)-net over F₉	[i]
19	No digital (4, 59, 45)-net over F₉	[i]
20	No digital (4, 60, 45)-net over F₉	[i]
21	No digital (4, 61, 45)-net over F₉	[i]
22	No digital (4, 62, 45)-net over F₉	[i]
23	No digital (4, 63, 45)-net over F₉	[i]
24	No digital (4, 64, 45)-net over F₉	[i]
25	No digital (4, 65, 45)-net over F₉	[i]
26	No digital (4, 66, 45)-net over F₉	[i]
27	No digital (4, 67, 45)-net over F₉	[i]
28	No digital (4, 68, 45)-net over F₉	[i]
29	No digital (4, 69, 45)-net over F₉	[i]
30	No digital (4, 70, 45)-net over F₉	[i]
31	No digital (4, 71, 45)-net over F₉	[i]
32	No digital (4, 72, 45)-net over F₉	[i]
33	No digital (4, 73, 45)-net over F₉	[i]
34	No digital (4, 74, 45)-net over F₉	[i]
35	No digital (4, 75, 45)-net over F₉	[i]
36	No digital (4, 76, 45)-net over F₉	[i]
37	No digital (4, 77, 45)-net over F₉	[i]
38	No digital (4, 78, 45)-net over F₉	[i]
39	No digital (4, 79, 45)-net over F₉	[i]
40	No digital (4, 80, 45)-net over F₉	[i]
41	No digital (4, 81, 45)-net over F₉	[i]
42	No digital (4, 82, 45)-net over F₉	[i]
43	No digital (4, 83, 45)-net over F₉	[i]
44	No digital (4, 84, 45)-net over F₉	[i]
45	No digital (4, 85, 45)-net over F₉	[i]
46	No digital (4, 86, 45)-net over F₉	[i]
47	No digital (4, 87, 45)-net over F₉	[i]
48	No digital (4, 88, 45)-net over F₉	[i]
49	No digital (4, 89, 45)-net over F₉	[i]
50	No digital (4, 90, 45)-net over F₉	[i]
51	No digital (4, 91, 45)-net over F₉	[i]
52	No digital (4, 92, 45)-net over F₉	[i]
53	No digital (4, 93, 45)-net over F₉	[i]
54	No digital (4, 94, 45)-net over F₉	[i]
55	No digital (4, 95, 45)-net over F₉	[i]
56	No digital (4, 96, 45)-net over F₉	[i]
57	No digital (4, 97, 45)-net over F₉	[i]
58	No digital (4, 98, 45)-net over F₉	[i]
59	No digital (4, 99, 45)-net over F₉	[i]
60	No digital (4, 100, 45)-net over F₉	[i]
61	No digital (4, 101, 45)-net over F₉	[i]
62	No digital (4, 102, 45)-net over F₉	[i]
63	No digital (4, 103, 45)-net over F₉	[i]
64	No digital (4, 104, 45)-net over F₉	[i]
65	No digital (4, 105, 45)-net over F₉	[i]
66	No digital (4, 106, 45)-net over F₉	[i]
67	No digital (4, 107, 45)-net over F₉	[i]
68	No digital (4, 108, 45)-net over F₉	[i]
69	No digital (4, 109, 45)-net over F₉	[i]
70	No digital (4, 110, 45)-net over F₉	[i]
71	No digital (4, 111, 45)-net over F₉	[i]
72	No digital (4, 112, 45)-net over F₉	[i]
73	No digital (4, 113, 45)-net over F₉	[i]
74	No digital (4, 114, 45)-net over F₉	[i]
75	No digital (4, 115, 45)-net over F₉	[i]
76	No digital (4, 116, 45)-net over F₉	[i]
77	No digital (4, 117, 45)-net over F₉	[i]
78	No digital (4, 118, 45)-net over F₉	[i]
79	No digital (4, 119, 45)-net over F₉	[i]
80	No digital (4, 120, 45)-net over F₉	[i]
81	No digital (4, 121, 45)-net over F₉	[i]
82	No digital (4, 122, 45)-net over F₉	[i]
83	No digital (4, 123, 45)-net over F₉	[i]
84	No digital (4, 124, 45)-net over F₉	[i]
85	No digital (4, 125, 45)-net over F₉	[i]
86	No digital (4, 126, 45)-net over F₉	[i]
87	No digital (4, 127, 45)-net over F₉	[i]
88	No digital (4, 128, 45)-net over F₉	[i]
89	No digital (4, 129, 45)-net over F₉	[i]
90	No digital (4, 130, 45)-net over F₉	[i]
91	No digital (4, 131, 45)-net over F₉	[i]
92	No digital (4, 132, 45)-net over F₉	[i]
93	No digital (4, 133, 45)-net over F₉	[i]
94	No digital (4, 134, 45)-net over F₉	[i]
95	No digital (4, 135, 45)-net over F₉	[i]
96	No digital (4, 136, 45)-net over F₉	[i]
97	No digital (4, 137, 45)-net over F₉	[i]
98	No digital (4, 138, 45)-net over F₉	[i]
99	No digital (4, 139, 45)-net over F₉	[i]
100	No digital (4, 140, 45)-net over F₉	[i]
101	No digital (4, 141, 45)-net over F₉	[i]
102	No digital (4, 142, 45)-net over F₉	[i]
103	No digital (4, 143, 45)-net over F₉	[i]
104	No digital (4, 144, 45)-net over F₉	[i]
105	No digital (4, 145, 45)-net over F₉	[i]
106	No digital (4, 146, 45)-net over F₉	[i]
107	No digital (4, 147, 45)-net over F₉	[i]
108	No digital (4, 148, 45)-net over F₉	[i]
109	No digital (4, 149, 45)-net over F₉	[i]
110	No digital (4, 150, 45)-net over F₉	[i]
111	No digital (4, m, 45)-net over F₉ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net