MinT - Information on Result #599065

Information on Result #599065

There is no digital (54, 162, 171)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3¹⁶², 171, F₃, 108) (dual of [171, 9, 109]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁶¹, 167, F₃, 108) (dual of [167, 6, 109]-code), but
  - residual code [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, 171, 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 (54, 163, 171)-net over F₃	[i]	m-Reduction
2	No digital (54, 164, 171)-net over F₃	[i]
3	No digital (54, 165, 171)-net over F₃	[i]
4	No digital (54, 166, 171)-net over F₃	[i]
5	No digital (54, 167, 171)-net over F₃	[i]
6	No digital (54, 168, 171)-net over F₃	[i]
7	No digital (54, 169, 171)-net over F₃	[i]
8	No digital (54, 170, 171)-net over F₃	[i]
9	No digital (54, 171, 171)-net over F₃	[i]
10	No digital (54, 172, 171)-net over F₃	[i]
11	No digital (54, 173, 171)-net over F₃	[i]
12	No digital (54, 174, 171)-net over F₃	[i]
13	No digital (54, 175, 171)-net over F₃	[i]
14	No digital (54, 176, 171)-net over F₃	[i]
15	No digital (54, 177, 171)-net over F₃	[i]
16	No digital (54, 178, 171)-net over F₃	[i]
17	No digital (54, 179, 171)-net over F₃	[i]
18	No digital (54, 180, 171)-net over F₃	[i]
19	No digital (54, 181, 171)-net over F₃	[i]
20	No digital (54, 182, 171)-net over F₃	[i]
21	No digital (54, 183, 171)-net over F₃	[i]
22	No digital (54, 184, 171)-net over F₃	[i]
23	No digital (54, 185, 171)-net over F₃	[i]
24	No digital (54, 186, 171)-net over F₃	[i]
25	No digital (54, 187, 171)-net over F₃	[i]
26	No digital (54, 188, 171)-net over F₃	[i]
27	No digital (54, 189, 171)-net over F₃	[i]
28	No digital (54, 190, 171)-net over F₃	[i]
29	No digital (54, 191, 171)-net over F₃	[i]
30	No digital (54, 192, 171)-net over F₃	[i]
31	No digital (54, 193, 171)-net over F₃	[i]
32	No digital (54, 194, 171)-net over F₃	[i]
33	No digital (54, 195, 171)-net over F₃	[i]
34	No digital (54, 196, 171)-net over F₃	[i]
35	No digital (54, 197, 171)-net over F₃	[i]
36	No digital (54, 198, 171)-net over F₃	[i]
37	No digital (54, 199, 171)-net over F₃	[i]
38	No digital (54, 200, 171)-net over F₃	[i]
39	No digital (54, 201, 171)-net over F₃	[i]
40	No digital (54, 202, 171)-net over F₃	[i]
41	No digital (54, 203, 171)-net over F₃	[i]
42	No digital (54, 204, 171)-net over F₃	[i]
43	No digital (54, 205, 171)-net over F₃	[i]
44	No digital (54, 206, 171)-net over F₃	[i]
45	No digital (54, 207, 171)-net over F₃	[i]
46	No digital (54, 208, 171)-net over F₃	[i]
47	No digital (54, 209, 171)-net over F₃	[i]
48	No digital (54, 210, 171)-net over F₃	[i]
49	No digital (54, 211, 171)-net over F₃	[i]
50	No digital (54, 212, 171)-net over F₃	[i]
51	No digital (54, 213, 171)-net over F₃	[i]
52	No digital (54, 214, 171)-net over F₃	[i]
53	No digital (54, 215, 171)-net over F₃	[i]
54	No digital (54, 216, 171)-net over F₃	[i]
55	No digital (54, 217, 171)-net over F₃	[i]
56	No digital (54, 218, 171)-net over F₃	[i]
57	No digital (54, 219, 171)-net over F₃	[i]
58	No digital (54, 220, 171)-net over F₃	[i]
59	No digital (54, 221, 171)-net over F₃	[i]
60	No digital (54, 222, 171)-net over F₃	[i]
61	No digital (54, 223, 171)-net over F₃	[i]
62	No digital (54, 224, 171)-net over F₃	[i]
63	No digital (54, 225, 171)-net over F₃	[i]
64	No digital (54, 226, 171)-net over F₃	[i]
65	No digital (54, 227, 171)-net over F₃	[i]
66	No digital (54, 228, 171)-net over F₃	[i]
67	No digital (54, 229, 171)-net over F₃	[i]
68	No digital (54, 230, 171)-net over F₃	[i]
69	No digital (54, 231, 171)-net over F₃	[i]
70	No digital (54, 232, 171)-net over F₃	[i]
71	No digital (54, 233, 171)-net over F₃	[i]
72	No digital (54, 234, 171)-net over F₃	[i]
73	No digital (54, 235, 171)-net over F₃	[i]
74	No digital (54, 236, 171)-net over F₃	[i]
75	No digital (54, 237, 171)-net over F₃	[i]
76	No digital (54, 238, 171)-net over F₃	[i]
77	No digital (54, 239, 171)-net over F₃	[i]
78	No digital (54, 240, 171)-net over F₃	[i]
79	No digital (54, 241, 171)-net over F₃	[i]
80	No digital (54, 242, 171)-net over F₃	[i]
81	No digital (54, 243, 171)-net over F₃	[i]
82	No digital (54, 244, 171)-net over F₃	[i]
83	No digital (54, 245, 171)-net over F₃	[i]
84	No digital (54, 246, 171)-net over F₃	[i]
85	No digital (54, 247, 171)-net over F₃	[i]
86	No digital (54, 248, 171)-net over F₃	[i]
87	No digital (54, 249, 171)-net over F₃	[i]
88	No digital (54, 250, 171)-net over F₃	[i]