MinT - Information on Result #599455

Information on Result #599455

There is no digital (43, 175, 181)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁷⁵, 181, F₄, 132) (dual of [181, 6, 133]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁷⁴, 178, F₄, 132) (dual of [178, 4, 133]-code), but
  - Griesmer bound [i]
2. linear OA(4⁶, 181, F₄, 3) (dual of [181, 175, 4]-code or 181-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 (43, 176, 181)-net over F₄	[i]	m-Reduction
2	No digital (43, 177, 181)-net over F₄	[i]
3	No digital (43, 178, 181)-net over F₄	[i]
4	No digital (43, 179, 181)-net over F₄	[i]
5	No digital (43, 180, 181)-net over F₄	[i]
6	No digital (43, 181, 181)-net over F₄	[i]
7	No digital (43, 182, 181)-net over F₄	[i]
8	No digital (43, 183, 181)-net over F₄	[i]
9	No digital (43, 184, 181)-net over F₄	[i]
10	No digital (43, 185, 181)-net over F₄	[i]
11	No digital (43, 186, 181)-net over F₄	[i]
12	No digital (43, 187, 181)-net over F₄	[i]
13	No digital (43, 188, 181)-net over F₄	[i]
14	No digital (43, 189, 181)-net over F₄	[i]
15	No digital (43, 190, 181)-net over F₄	[i]
16	No digital (43, 191, 181)-net over F₄	[i]
17	No digital (43, 192, 181)-net over F₄	[i]
18	No digital (43, 193, 181)-net over F₄	[i]
19	No digital (43, 194, 181)-net over F₄	[i]
20	No digital (43, 195, 181)-net over F₄	[i]
21	No digital (43, 196, 181)-net over F₄	[i]
22	No digital (43, 197, 181)-net over F₄	[i]
23	No digital (43, 198, 181)-net over F₄	[i]
24	No digital (43, 199, 181)-net over F₄	[i]
25	No digital (43, 200, 181)-net over F₄	[i]
26	No digital (43, 201, 181)-net over F₄	[i]
27	No digital (43, 202, 181)-net over F₄	[i]
28	No digital (43, 203, 181)-net over F₄	[i]
29	No digital (43, 204, 181)-net over F₄	[i]
30	No digital (43, 205, 181)-net over F₄	[i]
31	No digital (43, 206, 181)-net over F₄	[i]
32	No digital (43, 207, 181)-net over F₄	[i]
33	No digital (43, 208, 181)-net over F₄	[i]
34	No digital (43, 209, 181)-net over F₄	[i]
35	No digital (43, 210, 181)-net over F₄	[i]
36	No digital (43, 211, 181)-net over F₄	[i]
37	No digital (43, 212, 181)-net over F₄	[i]
38	No digital (43, 213, 181)-net over F₄	[i]
39	No digital (43, 214, 181)-net over F₄	[i]
40	No digital (43, 215, 181)-net over F₄	[i]
41	No digital (43, 216, 181)-net over F₄	[i]
42	No digital (43, 217, 181)-net over F₄	[i]
43	No digital (43, 218, 181)-net over F₄	[i]
44	No digital (43, 219, 181)-net over F₄	[i]
45	No digital (43, 220, 181)-net over F₄	[i]
46	No digital (43, 221, 181)-net over F₄	[i]
47	No digital (43, 222, 181)-net over F₄	[i]
48	No digital (43, 223, 181)-net over F₄	[i]
49	No digital (43, 224, 181)-net over F₄	[i]
50	No digital (43, 225, 181)-net over F₄	[i]
51	No digital (43, 226, 181)-net over F₄	[i]
52	No digital (43, 227, 181)-net over F₄	[i]
53	No digital (43, 228, 181)-net over F₄	[i]
54	No digital (43, 229, 181)-net over F₄	[i]
55	No digital (43, 230, 181)-net over F₄	[i]
56	No digital (43, 231, 181)-net over F₄	[i]
57	No digital (43, 232, 181)-net over F₄	[i]
58	No digital (43, 233, 181)-net over F₄	[i]
59	No digital (43, 234, 181)-net over F₄	[i]
60	No digital (43, 235, 181)-net over F₄	[i]
61	No digital (43, 236, 181)-net over F₄	[i]
62	No digital (43, 237, 181)-net over F₄	[i]
63	No digital (43, 238, 181)-net over F₄	[i]
64	No digital (43, 239, 181)-net over F₄	[i]
65	No digital (43, 240, 181)-net over F₄	[i]
66	No digital (43, 241, 181)-net over F₄	[i]
67	No digital (43, 242, 181)-net over F₄	[i]
68	No digital (43, 243, 181)-net over F₄	[i]
69	No digital (43, 244, 181)-net over F₄	[i]
70	No digital (43, 245, 181)-net over F₄	[i]
71	No digital (43, 246, 181)-net over F₄	[i]
72	No digital (43, 247, 181)-net over F₄	[i]
73	No digital (43, 248, 181)-net over F₄	[i]
74	No digital (43, 249, 181)-net over F₄	[i]
75	No digital (43, 250, 181)-net over F₄	[i]
76	No digital (43, 251, 181)-net over F₄	[i]
77	No digital (43, 252, 181)-net over F₄	[i]
78	No digital (43, 253, 181)-net over F₄	[i]
79	No digital (43, 254, 181)-net over F₄	[i]
80	No digital (43, 255, 181)-net over F₄	[i]
81	No digital (43, 256, 181)-net over F₄	[i]
82	No digital (43, 257, 181)-net over F₄	[i]
83	No digital (43, 258, 181)-net over F₄	[i]
84	No digital (43, 259, 181)-net over F₄	[i]
85	No digital (43, 260, 181)-net over F₄	[i]