MinT - Information on Result #599072

Information on Result #599072

There is no digital (55, 166, 175)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3¹⁶⁶, 175, F₃, 111) (dual of [175, 9, 112]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁶⁵, 171, F₃, 111) (dual of [171, 6, 112]-code), but
  - residual code [i] would yield linear OA(3⁵⁴, 59, F₃, 37) (dual of [59, 5, 38]-code), but
    - 1 times truncation [i] would yield linear OA(3⁵³, 58, F₃, 36) (dual of [58, 5, 37]-code), but
      - residual code [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, 175, 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 (55, 167, 175)-net over F₃	[i]	m-Reduction
2	No digital (55, 168, 175)-net over F₃	[i]
3	No digital (55, 169, 175)-net over F₃	[i]
4	No digital (55, 170, 175)-net over F₃	[i]
5	No digital (55, 171, 175)-net over F₃	[i]
6	No digital (55, 172, 175)-net over F₃	[i]
7	No digital (55, 173, 175)-net over F₃	[i]
8	No digital (55, 174, 175)-net over F₃	[i]
9	No digital (55, 175, 175)-net over F₃	[i]
10	No digital (55, 176, 175)-net over F₃	[i]
11	No digital (55, 177, 175)-net over F₃	[i]
12	No digital (55, 178, 175)-net over F₃	[i]
13	No digital (55, 179, 175)-net over F₃	[i]
14	No digital (55, 180, 175)-net over F₃	[i]
15	No digital (55, 181, 175)-net over F₃	[i]
16	No digital (55, 182, 175)-net over F₃	[i]
17	No digital (55, 183, 175)-net over F₃	[i]
18	No digital (55, 184, 175)-net over F₃	[i]
19	No digital (55, 185, 175)-net over F₃	[i]
20	No digital (55, 186, 175)-net over F₃	[i]
21	No digital (55, 187, 175)-net over F₃	[i]
22	No digital (55, 188, 175)-net over F₃	[i]
23	No digital (55, 189, 175)-net over F₃	[i]
24	No digital (55, 190, 175)-net over F₃	[i]
25	No digital (55, 191, 175)-net over F₃	[i]
26	No digital (55, 192, 175)-net over F₃	[i]
27	No digital (55, 193, 175)-net over F₃	[i]
28	No digital (55, 194, 175)-net over F₃	[i]
29	No digital (55, 195, 175)-net over F₃	[i]
30	No digital (55, 196, 175)-net over F₃	[i]
31	No digital (55, 197, 175)-net over F₃	[i]
32	No digital (55, 198, 175)-net over F₃	[i]
33	No digital (55, 199, 175)-net over F₃	[i]
34	No digital (55, 200, 175)-net over F₃	[i]
35	No digital (55, 201, 175)-net over F₃	[i]
36	No digital (55, 202, 175)-net over F₃	[i]
37	No digital (55, 203, 175)-net over F₃	[i]
38	No digital (55, 204, 175)-net over F₃	[i]
39	No digital (55, 205, 175)-net over F₃	[i]
40	No digital (55, 206, 175)-net over F₃	[i]
41	No digital (55, 207, 175)-net over F₃	[i]
42	No digital (55, 208, 175)-net over F₃	[i]
43	No digital (55, 209, 175)-net over F₃	[i]
44	No digital (55, 210, 175)-net over F₃	[i]
45	No digital (55, 211, 175)-net over F₃	[i]
46	No digital (55, 212, 175)-net over F₃	[i]
47	No digital (55, 213, 175)-net over F₃	[i]
48	No digital (55, 214, 175)-net over F₃	[i]
49	No digital (55, 215, 175)-net over F₃	[i]
50	No digital (55, 216, 175)-net over F₃	[i]
51	No digital (55, 217, 175)-net over F₃	[i]
52	No digital (55, 218, 175)-net over F₃	[i]
53	No digital (55, 219, 175)-net over F₃	[i]
54	No digital (55, 220, 175)-net over F₃	[i]
55	No digital (55, 221, 175)-net over F₃	[i]
56	No digital (55, 222, 175)-net over F₃	[i]
57	No digital (55, 223, 175)-net over F₃	[i]
58	No digital (55, 224, 175)-net over F₃	[i]
59	No digital (55, 225, 175)-net over F₃	[i]
60	No digital (55, 226, 175)-net over F₃	[i]
61	No digital (55, 227, 175)-net over F₃	[i]
62	No digital (55, 228, 175)-net over F₃	[i]
63	No digital (55, 229, 175)-net over F₃	[i]
64	No digital (55, 230, 175)-net over F₃	[i]
65	No digital (55, 231, 175)-net over F₃	[i]
66	No digital (55, 232, 175)-net over F₃	[i]
67	No digital (55, 233, 175)-net over F₃	[i]
68	No digital (55, 234, 175)-net over F₃	[i]
69	No digital (55, 235, 175)-net over F₃	[i]
70	No digital (55, 236, 175)-net over F₃	[i]
71	No digital (55, 237, 175)-net over F₃	[i]
72	No digital (55, 238, 175)-net over F₃	[i]
73	No digital (55, 239, 175)-net over F₃	[i]
74	No digital (55, 240, 175)-net over F₃	[i]
75	No digital (55, 241, 175)-net over F₃	[i]
76	No digital (55, 242, 175)-net over F₃	[i]
77	No digital (55, 243, 175)-net over F₃	[i]
78	No digital (55, 244, 175)-net over F₃	[i]
79	No digital (55, 245, 175)-net over F₃	[i]
80	No digital (55, 246, 175)-net over F₃	[i]
81	No digital (55, 247, 175)-net over F₃	[i]
82	No digital (55, 248, 175)-net over F₃	[i]
83	No digital (55, 249, 175)-net over F₃	[i]
84	No digital (55, 250, 175)-net over F₃	[i]