MinT - Information on Result #599104

Information on Result #599104

There is no digital (59, 179, 188)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3¹⁷⁹, 188, F₃, 120) (dual of [188, 9, 121]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁷⁸, 184, F₃, 120) (dual of [184, 6, 121]-code), but
  - residual code [i] would yield linear OA(3⁵⁸, 63, F₃, 40) (dual of [63, 5, 41]-code), but
    - 1 times truncation [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, 188, 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 (59, 180, 188)-net over F₃	[i]	m-Reduction
2	No digital (59, 181, 188)-net over F₃	[i]
3	No digital (59, 182, 188)-net over F₃	[i]
4	No digital (59, 183, 188)-net over F₃	[i]
5	No digital (59, 184, 188)-net over F₃	[i]
6	No digital (59, 185, 188)-net over F₃	[i]
7	No digital (59, 186, 188)-net over F₃	[i]
8	No digital (59, 187, 188)-net over F₃	[i]
9	No digital (59, 188, 188)-net over F₃	[i]
10	No digital (59, 189, 188)-net over F₃	[i]
11	No digital (59, 190, 188)-net over F₃	[i]
12	No digital (59, 191, 188)-net over F₃	[i]
13	No digital (59, 192, 188)-net over F₃	[i]
14	No digital (59, 193, 188)-net over F₃	[i]
15	No digital (59, 194, 188)-net over F₃	[i]
16	No digital (59, 195, 188)-net over F₃	[i]
17	No digital (59, 196, 188)-net over F₃	[i]
18	No digital (59, 197, 188)-net over F₃	[i]
19	No digital (59, 198, 188)-net over F₃	[i]
20	No digital (59, 199, 188)-net over F₃	[i]
21	No digital (59, 200, 188)-net over F₃	[i]
22	No digital (59, 201, 188)-net over F₃	[i]
23	No digital (59, 202, 188)-net over F₃	[i]
24	No digital (59, 203, 188)-net over F₃	[i]
25	No digital (59, 204, 188)-net over F₃	[i]
26	No digital (59, 205, 188)-net over F₃	[i]
27	No digital (59, 206, 188)-net over F₃	[i]
28	No digital (59, 207, 188)-net over F₃	[i]
29	No digital (59, 208, 188)-net over F₃	[i]
30	No digital (59, 209, 188)-net over F₃	[i]
31	No digital (59, 210, 188)-net over F₃	[i]
32	No digital (59, 211, 188)-net over F₃	[i]
33	No digital (59, 212, 188)-net over F₃	[i]
34	No digital (59, 213, 188)-net over F₃	[i]
35	No digital (59, 214, 188)-net over F₃	[i]
36	No digital (59, 215, 188)-net over F₃	[i]
37	No digital (59, 216, 188)-net over F₃	[i]
38	No digital (59, 217, 188)-net over F₃	[i]
39	No digital (59, 218, 188)-net over F₃	[i]
40	No digital (59, 219, 188)-net over F₃	[i]
41	No digital (59, 220, 188)-net over F₃	[i]
42	No digital (59, 221, 188)-net over F₃	[i]
43	No digital (59, 222, 188)-net over F₃	[i]
44	No digital (59, 223, 188)-net over F₃	[i]
45	No digital (59, 224, 188)-net over F₃	[i]
46	No digital (59, 225, 188)-net over F₃	[i]
47	No digital (59, 226, 188)-net over F₃	[i]
48	No digital (59, 227, 188)-net over F₃	[i]
49	No digital (59, 228, 188)-net over F₃	[i]
50	No digital (59, 229, 188)-net over F₃	[i]
51	No digital (59, 230, 188)-net over F₃	[i]
52	No digital (59, 231, 188)-net over F₃	[i]
53	No digital (59, 232, 188)-net over F₃	[i]
54	No digital (59, 233, 188)-net over F₃	[i]
55	No digital (59, 234, 188)-net over F₃	[i]
56	No digital (59, 235, 188)-net over F₃	[i]
57	No digital (59, 236, 188)-net over F₃	[i]
58	No digital (59, 237, 188)-net over F₃	[i]
59	No digital (59, 238, 188)-net over F₃	[i]
60	No digital (59, 239, 188)-net over F₃	[i]
61	No digital (59, 240, 188)-net over F₃	[i]
62	No digital (59, 241, 188)-net over F₃	[i]
63	No digital (59, 242, 188)-net over F₃	[i]
64	No digital (59, 243, 188)-net over F₃	[i]
65	No digital (59, 244, 188)-net over F₃	[i]
66	No digital (59, 245, 188)-net over F₃	[i]
67	No digital (59, 246, 188)-net over F₃	[i]
68	No digital (59, 247, 188)-net over F₃	[i]
69	No digital (59, 248, 188)-net over F₃	[i]
70	No digital (59, 249, 188)-net over F₃	[i]
71	No digital (59, 250, 188)-net over F₃	[i]