MinT - Information on Result #599448

Information on Result #599448

There is no digital (42, 170, 176)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁷⁰, 176, F₄, 128) (dual of [176, 6, 129]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁶⁹, 173, F₄, 128) (dual of [173, 4, 129]-code), but
  - Griesmer bound [i]
2. linear OA(4⁶, 176, F₄, 3) (dual of [176, 170, 4]-code or 176-cap in PG(5,4)), but
  - discarding factors / shortening the dual code would yield linear OA(4⁶, 160, F₄, 3) (dual of [160, 154, 4]-code or 160-cap in PG(5,4)), but
    - 1 times Hill recurrence [i] would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
      - 41 is the largest size of a cap in PG(4,Â 4) [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 (42, 171, 176)-net over F₄	[i]	m-Reduction
2	No digital (42, 172, 176)-net over F₄	[i]
3	No digital (42, 173, 176)-net over F₄	[i]
4	No digital (42, 174, 176)-net over F₄	[i]
5	No digital (42, 175, 176)-net over F₄	[i]
6	No digital (42, 176, 176)-net over F₄	[i]
7	No digital (42, 177, 176)-net over F₄	[i]
8	No digital (42, 178, 176)-net over F₄	[i]
9	No digital (42, 179, 176)-net over F₄	[i]
10	No digital (42, 180, 176)-net over F₄	[i]
11	No digital (42, 181, 176)-net over F₄	[i]
12	No digital (42, 182, 176)-net over F₄	[i]
13	No digital (42, 183, 176)-net over F₄	[i]
14	No digital (42, 184, 176)-net over F₄	[i]
15	No digital (42, 185, 176)-net over F₄	[i]
16	No digital (42, 186, 176)-net over F₄	[i]
17	No digital (42, 187, 176)-net over F₄	[i]
18	No digital (42, 188, 176)-net over F₄	[i]
19	No digital (42, 189, 176)-net over F₄	[i]
20	No digital (42, 190, 176)-net over F₄	[i]
21	No digital (42, 191, 176)-net over F₄	[i]
22	No digital (42, 192, 176)-net over F₄	[i]
23	No digital (42, 193, 176)-net over F₄	[i]
24	No digital (42, 194, 176)-net over F₄	[i]
25	No digital (42, 195, 176)-net over F₄	[i]
26	No digital (42, 196, 176)-net over F₄	[i]
27	No digital (42, 197, 176)-net over F₄	[i]
28	No digital (42, 198, 176)-net over F₄	[i]
29	No digital (42, 199, 176)-net over F₄	[i]
30	No digital (42, 200, 176)-net over F₄	[i]
31	No digital (42, 201, 176)-net over F₄	[i]
32	No digital (42, 202, 176)-net over F₄	[i]
33	No digital (42, 203, 176)-net over F₄	[i]
34	No digital (42, 204, 176)-net over F₄	[i]
35	No digital (42, 205, 176)-net over F₄	[i]
36	No digital (42, 206, 176)-net over F₄	[i]
37	No digital (42, 207, 176)-net over F₄	[i]
38	No digital (42, 208, 176)-net over F₄	[i]
39	No digital (42, 209, 176)-net over F₄	[i]
40	No digital (42, 210, 176)-net over F₄	[i]
41	No digital (42, 211, 176)-net over F₄	[i]
42	No digital (42, 212, 176)-net over F₄	[i]
43	No digital (42, 213, 176)-net over F₄	[i]
44	No digital (42, 214, 176)-net over F₄	[i]
45	No digital (42, 215, 176)-net over F₄	[i]
46	No digital (42, 216, 176)-net over F₄	[i]
47	No digital (42, 217, 176)-net over F₄	[i]
48	No digital (42, 218, 176)-net over F₄	[i]
49	No digital (42, 219, 176)-net over F₄	[i]
50	No digital (42, 220, 176)-net over F₄	[i]
51	No digital (42, 221, 176)-net over F₄	[i]
52	No digital (42, 222, 176)-net over F₄	[i]
53	No digital (42, 223, 176)-net over F₄	[i]
54	No digital (42, 224, 176)-net over F₄	[i]
55	No digital (42, 225, 176)-net over F₄	[i]
56	No digital (42, 226, 176)-net over F₄	[i]
57	No digital (42, 227, 176)-net over F₄	[i]
58	No digital (42, 228, 176)-net over F₄	[i]
59	No digital (42, 229, 176)-net over F₄	[i]
60	No digital (42, 230, 176)-net over F₄	[i]
61	No digital (42, 231, 176)-net over F₄	[i]
62	No digital (42, 232, 176)-net over F₄	[i]
63	No digital (42, 233, 176)-net over F₄	[i]
64	No digital (42, 234, 176)-net over F₄	[i]
65	No digital (42, 235, 176)-net over F₄	[i]
66	No digital (42, 236, 176)-net over F₄	[i]
67	No digital (42, 237, 176)-net over F₄	[i]
68	No digital (42, 238, 176)-net over F₄	[i]
69	No digital (42, 239, 176)-net over F₄	[i]
70	No digital (42, 240, 176)-net over F₄	[i]
71	No digital (42, 241, 176)-net over F₄	[i]
72	No digital (42, 242, 176)-net over F₄	[i]
73	No digital (42, 243, 176)-net over F₄	[i]
74	No digital (42, 244, 176)-net over F₄	[i]
75	No digital (42, 245, 176)-net over F₄	[i]
76	No digital (42, 246, 176)-net over F₄	[i]
77	No digital (42, 247, 176)-net over F₄	[i]
78	No digital (42, 248, 176)-net over F₄	[i]
79	No digital (42, 249, 176)-net over F₄	[i]
80	No digital (42, 250, 176)-net over F₄	[i]
81	No digital (42, 251, 176)-net over F₄	[i]
82	No digital (42, 252, 176)-net over F₄	[i]
83	No digital (42, 253, 176)-net over F₄	[i]
84	No digital (42, 254, 176)-net over F₄	[i]
85	No digital (42, 255, 176)-net over F₄	[i]
86	No digital (42, 256, 176)-net over F₄	[i]
87	No digital (42, 257, 176)-net over F₄	[i]
88	No digital (42, 258, 176)-net over F₄	[i]
89	No digital (42, 259, 176)-net over F₄	[i]
90	No digital (42, 260, 176)-net over F₄	[i]