MinT - Information on Result #598990

Information on Result #598990

There is no digital (36, 108, 117)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3¹⁰⁸, 117, F₃, 72) (dual of [117, 9, 73]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁰⁷, 113, F₃, 72) (dual of [113, 6, 73]-code), but
  - residual code [i] would yield linear OA(3³⁵, 40, F₃, 24) (dual of [40, 5, 25]-code), but
    - â€œvE1â€ bound on codes from Brouwerâ€™s database [i]
2. OA(3⁹, 117, S₃, 4), but
  - discarding factors would yield OA(3⁹, 100, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 20001 > 3⁹ [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 (36, 109, 117)-net over F₃	[i]	m-Reduction
2	No digital (36, 110, 117)-net over F₃	[i]
3	No digital (36, 111, 117)-net over F₃	[i]
4	No digital (36, 112, 117)-net over F₃	[i]
5	No digital (36, 113, 117)-net over F₃	[i]
6	No digital (36, 114, 117)-net over F₃	[i]
7	No digital (36, 115, 117)-net over F₃	[i]
8	No digital (36, 116, 117)-net over F₃	[i]
9	No digital (36, 117, 117)-net over F₃	[i]
10	No digital (36, 118, 117)-net over F₃	[i]
11	No digital (36, 119, 117)-net over F₃	[i]
12	No digital (36, 120, 117)-net over F₃	[i]
13	No digital (36, 121, 117)-net over F₃	[i]
14	No digital (36, 122, 117)-net over F₃	[i]
15	No digital (36, 123, 117)-net over F₃	[i]
16	No digital (36, 124, 117)-net over F₃	[i]
17	No digital (36, 125, 117)-net over F₃	[i]
18	No digital (36, 126, 117)-net over F₃	[i]
19	No digital (36, 127, 117)-net over F₃	[i]
20	No digital (36, 128, 117)-net over F₃	[i]
21	No digital (36, 129, 117)-net over F₃	[i]
22	No digital (36, 130, 117)-net over F₃	[i]
23	No digital (36, 131, 117)-net over F₃	[i]
24	No digital (36, 132, 117)-net over F₃	[i]
25	No digital (36, 133, 117)-net over F₃	[i]
26	No digital (36, 134, 117)-net over F₃	[i]
27	No digital (36, 135, 117)-net over F₃	[i]
28	No digital (36, 136, 117)-net over F₃	[i]
29	No digital (36, 137, 117)-net over F₃	[i]
30	No digital (36, 138, 117)-net over F₃	[i]
31	No digital (36, 139, 117)-net over F₃	[i]
32	No digital (36, 140, 117)-net over F₃	[i]
33	No digital (36, 141, 117)-net over F₃	[i]
34	No digital (36, 142, 117)-net over F₃	[i]
35	No digital (36, 143, 117)-net over F₃	[i]
36	No digital (36, 144, 117)-net over F₃	[i]
37	No digital (36, 145, 117)-net over F₃	[i]
38	No digital (36, 146, 117)-net over F₃	[i]
39	No digital (36, 147, 117)-net over F₃	[i]
40	No digital (36, 148, 117)-net over F₃	[i]
41	No digital (36, 149, 117)-net over F₃	[i]
42	No digital (36, 150, 117)-net over F₃	[i]
43	No digital (36, 151, 117)-net over F₃	[i]
44	No digital (36, 152, 117)-net over F₃	[i]
45	No digital (36, 153, 117)-net over F₃	[i]
46	No digital (36, 154, 117)-net over F₃	[i]
47	No digital (36, 155, 117)-net over F₃	[i]
48	No digital (36, 156, 117)-net over F₃	[i]
49	No digital (36, 157, 117)-net over F₃	[i]
50	No digital (36, 158, 117)-net over F₃	[i]
51	No digital (36, 159, 117)-net over F₃	[i]
52	No digital (36, 160, 117)-net over F₃	[i]
53	No digital (36, 161, 117)-net over F₃	[i]
54	No digital (36, 162, 117)-net over F₃	[i]
55	No digital (36, 163, 117)-net over F₃	[i]
56	No digital (36, 164, 117)-net over F₃	[i]
57	No digital (36, 165, 117)-net over F₃	[i]
58	No digital (36, 166, 117)-net over F₃	[i]
59	No digital (36, 167, 117)-net over F₃	[i]
60	No digital (36, 168, 117)-net over F₃	[i]
61	No digital (36, 169, 117)-net over F₃	[i]
62	No digital (36, 170, 117)-net over F₃	[i]
63	No digital (36, 171, 117)-net over F₃	[i]
64	No digital (36, 172, 117)-net over F₃	[i]
65	No digital (36, 173, 117)-net over F₃	[i]
66	No digital (36, 174, 117)-net over F₃	[i]
67	No digital (36, 175, 117)-net over F₃	[i]
68	No digital (36, 176, 117)-net over F₃	[i]
69	No digital (36, 177, 117)-net over F₃	[i]