MinT - Information on Result #599088

Information on Result #599088

There is no digital (57, 174, 180)-net over F₃, because extracting embedded orthogonal array would yield 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]

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