MinT - Information on Result #599420

Information on Result #599420

There is no digital (38, 154, 162)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁵⁴, 162, F₄, 116) (dual of [162, 8, 117]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁵³, 158, F₄, 116) (dual of [158, 5, 117]-code), but
  - residual code [i] would yield linear OA(4³⁷, 41, F₄, 29) (dual of [41, 4, 30]-code), but
    - 1 times truncation [i] would yield linear OA(4³⁶, 40, F₄, 28) (dual of [40, 4, 29]-code), but
      - residual code [i] would yield linear OA(4⁸, 11, F₄, 7) (dual of [11, 3, 8]-code), but
        improvement by Maruta on the Griesmer bound [i]
2. OA(4⁸, 162, S₄, 4), but
  - discarding factors would yield OA(4⁸, 121, S₄, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 65704 > 4⁸ [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 (38, 155, 162)-net over F₄	[i]	m-Reduction
2	No digital (38, 156, 162)-net over F₄	[i]
3	No digital (38, 157, 162)-net over F₄	[i]
4	No digital (38, 158, 162)-net over F₄	[i]
5	No digital (38, 159, 162)-net over F₄	[i]
6	No digital (38, 160, 162)-net over F₄	[i]
7	No digital (38, 161, 162)-net over F₄	[i]
8	No digital (38, 162, 162)-net over F₄	[i]
9	No digital (38, 163, 162)-net over F₄	[i]
10	No digital (38, 164, 162)-net over F₄	[i]
11	No digital (38, 165, 162)-net over F₄	[i]
12	No digital (38, 166, 162)-net over F₄	[i]
13	No digital (38, 167, 162)-net over F₄	[i]
14	No digital (38, 168, 162)-net over F₄	[i]
15	No digital (38, 169, 162)-net over F₄	[i]
16	No digital (38, 170, 162)-net over F₄	[i]
17	No digital (38, 171, 162)-net over F₄	[i]
18	No digital (38, 172, 162)-net over F₄	[i]
19	No digital (38, 173, 162)-net over F₄	[i]
20	No digital (38, 174, 162)-net over F₄	[i]
21	No digital (38, 175, 162)-net over F₄	[i]
22	No digital (38, 176, 162)-net over F₄	[i]
23	No digital (38, 177, 162)-net over F₄	[i]
24	No digital (38, 178, 162)-net over F₄	[i]
25	No digital (38, 179, 162)-net over F₄	[i]
26	No digital (38, 180, 162)-net over F₄	[i]
27	No digital (38, 181, 162)-net over F₄	[i]
28	No digital (38, 182, 162)-net over F₄	[i]
29	No digital (38, 183, 162)-net over F₄	[i]
30	No digital (38, 184, 162)-net over F₄	[i]
31	No digital (38, 185, 162)-net over F₄	[i]
32	No digital (38, 186, 162)-net over F₄	[i]
33	No digital (38, 187, 162)-net over F₄	[i]
34	No digital (38, 188, 162)-net over F₄	[i]
35	No digital (38, 189, 162)-net over F₄	[i]
36	No digital (38, 190, 162)-net over F₄	[i]
37	No digital (38, 191, 162)-net over F₄	[i]
38	No digital (38, 192, 162)-net over F₄	[i]
39	No digital (38, 193, 162)-net over F₄	[i]
40	No digital (38, 194, 162)-net over F₄	[i]
41	No digital (38, 195, 162)-net over F₄	[i]
42	No digital (38, 196, 162)-net over F₄	[i]
43	No digital (38, 197, 162)-net over F₄	[i]
44	No digital (38, 198, 162)-net over F₄	[i]
45	No digital (38, 199, 162)-net over F₄	[i]
46	No digital (38, 200, 162)-net over F₄	[i]
47	No digital (38, 201, 162)-net over F₄	[i]
48	No digital (38, 202, 162)-net over F₄	[i]
49	No digital (38, 203, 162)-net over F₄	[i]
50	No digital (38, 204, 162)-net over F₄	[i]
51	No digital (38, 205, 162)-net over F₄	[i]
52	No digital (38, 206, 162)-net over F₄	[i]
53	No digital (38, 207, 162)-net over F₄	[i]
54	No digital (38, 208, 162)-net over F₄	[i]
55	No digital (38, 209, 162)-net over F₄	[i]
56	No digital (38, 210, 162)-net over F₄	[i]
57	No digital (38, 211, 162)-net over F₄	[i]
58	No digital (38, 212, 162)-net over F₄	[i]
59	No digital (38, 213, 162)-net over F₄	[i]
60	No digital (38, 214, 162)-net over F₄	[i]
61	No digital (38, 215, 162)-net over F₄	[i]
62	No digital (38, 216, 162)-net over F₄	[i]
63	No digital (38, 217, 162)-net over F₄	[i]
64	No digital (38, 218, 162)-net over F₄	[i]
65	No digital (38, 219, 162)-net over F₄	[i]
66	No digital (38, 220, 162)-net over F₄	[i]
67	No digital (38, 221, 162)-net over F₄	[i]
68	No digital (38, 222, 162)-net over F₄	[i]
69	No digital (38, 223, 162)-net over F₄	[i]
70	No digital (38, 224, 162)-net over F₄	[i]
71	No digital (38, 225, 162)-net over F₄	[i]
72	No digital (38, 226, 162)-net over F₄	[i]
73	No digital (38, 227, 162)-net over F₄	[i]
74	No digital (38, 228, 162)-net over F₄	[i]
75	No digital (38, 229, 162)-net over F₄	[i]
76	No digital (38, 230, 162)-net over F₄	[i]
77	No digital (38, 231, 162)-net over F₄	[i]
78	No digital (38, 232, 162)-net over F₄	[i]
79	No digital (38, 233, 162)-net over F₄	[i]
80	No digital (38, 234, 162)-net over F₄	[i]
81	No digital (38, 235, 162)-net over F₄	[i]
82	No digital (38, 236, 162)-net over F₄	[i]
83	No digital (38, 237, 162)-net over F₄	[i]
84	No digital (38, 238, 162)-net over F₄	[i]
85	No digital (38, 239, 162)-net over F₄	[i]
86	No digital (38, 240, 162)-net over F₄	[i]
87	No digital (38, 241, 162)-net over F₄	[i]
88	No digital (38, 242, 162)-net over F₄	[i]
89	No digital (38, 243, 162)-net over F₄	[i]
90	No digital (38, 244, 162)-net over F₄	[i]
91	No digital (38, 245, 162)-net over F₄	[i]
92	No digital (38, 246, 162)-net over F₄	[i]
93	No digital (38, 247, 162)-net over F₄	[i]
94	No digital (38, 248, 162)-net over F₄	[i]
95	No digital (38, 249, 162)-net over F₄	[i]
96	No digital (38, 250, 162)-net over F₄	[i]
97	No digital (38, 251, 162)-net over F₄	[i]
98	No digital (38, 252, 162)-net over F₄	[i]
99	No digital (38, 253, 162)-net over F₄	[i]
100	No digital (38, 254, 162)-net over F₄	[i]
101	No digital (38, 255, 162)-net over F₄	[i]
102	No digital (38, 256, 162)-net over F₄	[i]
103	No digital (38, 257, 162)-net over F₄	[i]
104	No digital (38, 258, 162)-net over F₄	[i]
105	No digital (38, 259, 162)-net over F₄	[i]
106	No digital (38, 260, 162)-net over F₄	[i]