MinT - Information on Result #599096

Information on Result #599096

There is no digital (58, 175, 184)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3¹⁷⁵, 184, F₃, 117) (dual of [184, 9, 118]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁷⁴, 180, F₃, 117) (dual of [180, 6, 118]-code), but
  - residual code [i] would yield linear OA(3⁵⁷, 62, F₃, 39) (dual of [62, 5, 40]-code), but
    - residual code [i] would yield linear OA(3¹⁸, 22, F₃, 13) (dual of [22, 4, 14]-code), but
      - 1 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3⁹, 184, 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 (58, 176, 184)-net over F₃	[i]	m-Reduction
2	No digital (58, 177, 184)-net over F₃	[i]
3	No digital (58, 178, 184)-net over F₃	[i]
4	No digital (58, 179, 184)-net over F₃	[i]
5	No digital (58, 180, 184)-net over F₃	[i]
6	No digital (58, 181, 184)-net over F₃	[i]
7	No digital (58, 182, 184)-net over F₃	[i]
8	No digital (58, 183, 184)-net over F₃	[i]
9	No digital (58, 184, 184)-net over F₃	[i]
10	No digital (58, 185, 184)-net over F₃	[i]
11	No digital (58, 186, 184)-net over F₃	[i]
12	No digital (58, 187, 184)-net over F₃	[i]
13	No digital (58, 188, 184)-net over F₃	[i]
14	No digital (58, 189, 184)-net over F₃	[i]
15	No digital (58, 190, 184)-net over F₃	[i]
16	No digital (58, 191, 184)-net over F₃	[i]
17	No digital (58, 192, 184)-net over F₃	[i]
18	No digital (58, 193, 184)-net over F₃	[i]
19	No digital (58, 194, 184)-net over F₃	[i]
20	No digital (58, 195, 184)-net over F₃	[i]
21	No digital (58, 196, 184)-net over F₃	[i]
22	No digital (58, 197, 184)-net over F₃	[i]
23	No digital (58, 198, 184)-net over F₃	[i]
24	No digital (58, 199, 184)-net over F₃	[i]
25	No digital (58, 200, 184)-net over F₃	[i]
26	No digital (58, 201, 184)-net over F₃	[i]
27	No digital (58, 202, 184)-net over F₃	[i]
28	No digital (58, 203, 184)-net over F₃	[i]
29	No digital (58, 204, 184)-net over F₃	[i]
30	No digital (58, 205, 184)-net over F₃	[i]
31	No digital (58, 206, 184)-net over F₃	[i]
32	No digital (58, 207, 184)-net over F₃	[i]
33	No digital (58, 208, 184)-net over F₃	[i]
34	No digital (58, 209, 184)-net over F₃	[i]
35	No digital (58, 210, 184)-net over F₃	[i]
36	No digital (58, 211, 184)-net over F₃	[i]
37	No digital (58, 212, 184)-net over F₃	[i]
38	No digital (58, 213, 184)-net over F₃	[i]
39	No digital (58, 214, 184)-net over F₃	[i]
40	No digital (58, 215, 184)-net over F₃	[i]
41	No digital (58, 216, 184)-net over F₃	[i]
42	No digital (58, 217, 184)-net over F₃	[i]
43	No digital (58, 218, 184)-net over F₃	[i]
44	No digital (58, 219, 184)-net over F₃	[i]
45	No digital (58, 220, 184)-net over F₃	[i]
46	No digital (58, 221, 184)-net over F₃	[i]
47	No digital (58, 222, 184)-net over F₃	[i]
48	No digital (58, 223, 184)-net over F₃	[i]
49	No digital (58, 224, 184)-net over F₃	[i]
50	No digital (58, 225, 184)-net over F₃	[i]
51	No digital (58, 226, 184)-net over F₃	[i]
52	No digital (58, 227, 184)-net over F₃	[i]
53	No digital (58, 228, 184)-net over F₃	[i]
54	No digital (58, 229, 184)-net over F₃	[i]
55	No digital (58, 230, 184)-net over F₃	[i]
56	No digital (58, 231, 184)-net over F₃	[i]
57	No digital (58, 232, 184)-net over F₃	[i]
58	No digital (58, 233, 184)-net over F₃	[i]
59	No digital (58, 234, 184)-net over F₃	[i]
60	No digital (58, 235, 184)-net over F₃	[i]
61	No digital (58, 236, 184)-net over F₃	[i]
62	No digital (58, 237, 184)-net over F₃	[i]
63	No digital (58, 238, 184)-net over F₃	[i]
64	No digital (58, 239, 184)-net over F₃	[i]
65	No digital (58, 240, 184)-net over F₃	[i]
66	No digital (58, 241, 184)-net over F₃	[i]
67	No digital (58, 242, 184)-net over F₃	[i]
68	No digital (58, 243, 184)-net over F₃	[i]
69	No digital (58, 244, 184)-net over F₃	[i]
70	No digital (58, 245, 184)-net over F₃	[i]
71	No digital (58, 246, 184)-net over F₃	[i]
72	No digital (58, 247, 184)-net over F₃	[i]
73	No digital (58, 248, 184)-net over F₃	[i]
74	No digital (58, 249, 184)-net over F₃	[i]
75	No digital (58, 250, 184)-net over F₃	[i]