MinT - Information on Result #599462

Information on Result #599462

There is no digital (44, 180, 186)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁸⁰, 186, F₄, 136) (dual of [186, 6, 137]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁷⁹, 183, F₄, 136) (dual of [183, 4, 137]-code), but
  - Griesmer bound [i]
2. linear OA(4⁶, 186, F₄, 3) (dual of [186, 180, 4]-code or 186-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 (44, 181, 186)-net over F₄	[i]	m-Reduction
2	No digital (44, 182, 186)-net over F₄	[i]
3	No digital (44, 183, 186)-net over F₄	[i]
4	No digital (44, 184, 186)-net over F₄	[i]
5	No digital (44, 185, 186)-net over F₄	[i]
6	No digital (44, 186, 186)-net over F₄	[i]
7	No digital (44, 187, 186)-net over F₄	[i]
8	No digital (44, 188, 186)-net over F₄	[i]
9	No digital (44, 189, 186)-net over F₄	[i]
10	No digital (44, 190, 186)-net over F₄	[i]
11	No digital (44, 191, 186)-net over F₄	[i]
12	No digital (44, 192, 186)-net over F₄	[i]
13	No digital (44, 193, 186)-net over F₄	[i]
14	No digital (44, 194, 186)-net over F₄	[i]
15	No digital (44, 195, 186)-net over F₄	[i]
16	No digital (44, 196, 186)-net over F₄	[i]
17	No digital (44, 197, 186)-net over F₄	[i]
18	No digital (44, 198, 186)-net over F₄	[i]
19	No digital (44, 199, 186)-net over F₄	[i]
20	No digital (44, 200, 186)-net over F₄	[i]
21	No digital (44, 201, 186)-net over F₄	[i]
22	No digital (44, 202, 186)-net over F₄	[i]
23	No digital (44, 203, 186)-net over F₄	[i]
24	No digital (44, 204, 186)-net over F₄	[i]
25	No digital (44, 205, 186)-net over F₄	[i]
26	No digital (44, 206, 186)-net over F₄	[i]
27	No digital (44, 207, 186)-net over F₄	[i]
28	No digital (44, 208, 186)-net over F₄	[i]
29	No digital (44, 209, 186)-net over F₄	[i]
30	No digital (44, 210, 186)-net over F₄	[i]
31	No digital (44, 211, 186)-net over F₄	[i]
32	No digital (44, 212, 186)-net over F₄	[i]
33	No digital (44, 213, 186)-net over F₄	[i]
34	No digital (44, 214, 186)-net over F₄	[i]
35	No digital (44, 215, 186)-net over F₄	[i]
36	No digital (44, 216, 186)-net over F₄	[i]
37	No digital (44, 217, 186)-net over F₄	[i]
38	No digital (44, 218, 186)-net over F₄	[i]
39	No digital (44, 219, 186)-net over F₄	[i]
40	No digital (44, 220, 186)-net over F₄	[i]
41	No digital (44, 221, 186)-net over F₄	[i]
42	No digital (44, 222, 186)-net over F₄	[i]
43	No digital (44, 223, 186)-net over F₄	[i]
44	No digital (44, 224, 186)-net over F₄	[i]
45	No digital (44, 225, 186)-net over F₄	[i]
46	No digital (44, 226, 186)-net over F₄	[i]
47	No digital (44, 227, 186)-net over F₄	[i]
48	No digital (44, 228, 186)-net over F₄	[i]
49	No digital (44, 229, 186)-net over F₄	[i]
50	No digital (44, 230, 186)-net over F₄	[i]
51	No digital (44, 231, 186)-net over F₄	[i]
52	No digital (44, 232, 186)-net over F₄	[i]
53	No digital (44, 233, 186)-net over F₄	[i]
54	No digital (44, 234, 186)-net over F₄	[i]
55	No digital (44, 235, 186)-net over F₄	[i]
56	No digital (44, 236, 186)-net over F₄	[i]
57	No digital (44, 237, 186)-net over F₄	[i]
58	No digital (44, 238, 186)-net over F₄	[i]
59	No digital (44, 239, 186)-net over F₄	[i]
60	No digital (44, 240, 186)-net over F₄	[i]
61	No digital (44, 241, 186)-net over F₄	[i]
62	No digital (44, 242, 186)-net over F₄	[i]
63	No digital (44, 243, 186)-net over F₄	[i]
64	No digital (44, 244, 186)-net over F₄	[i]
65	No digital (44, 245, 186)-net over F₄	[i]
66	No digital (44, 246, 186)-net over F₄	[i]
67	No digital (44, 247, 186)-net over F₄	[i]
68	No digital (44, 248, 186)-net over F₄	[i]
69	No digital (44, 249, 186)-net over F₄	[i]
70	No digital (44, 250, 186)-net over F₄	[i]
71	No digital (44, 251, 186)-net over F₄	[i]
72	No digital (44, 252, 186)-net over F₄	[i]
73	No digital (44, 253, 186)-net over F₄	[i]
74	No digital (44, 254, 186)-net over F₄	[i]
75	No digital (44, 255, 186)-net over F₄	[i]
76	No digital (44, 256, 186)-net over F₄	[i]
77	No digital (44, 257, 186)-net over F₄	[i]
78	No digital (44, 258, 186)-net over F₄	[i]
79	No digital (44, 259, 186)-net over F₄	[i]
80	No digital (44, 260, 186)-net over F₄	[i]