MinT - Information on Result #599412

Information on Result #599412

There is no digital (37, 149, 157)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁴⁹, 157, F₄, 112) (dual of [157, 8, 113]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁴⁸, 153, F₄, 112) (dual of [153, 5, 113]-code), but
  - residual code [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, 157, 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 (37, 150, 157)-net over F₄	[i]	m-Reduction
2	No digital (37, 151, 157)-net over F₄	[i]
3	No digital (37, 152, 157)-net over F₄	[i]
4	No digital (37, 153, 157)-net over F₄	[i]
5	No digital (37, 154, 157)-net over F₄	[i]
6	No digital (37, 155, 157)-net over F₄	[i]
7	No digital (37, 156, 157)-net over F₄	[i]
8	No digital (37, 157, 157)-net over F₄	[i]
9	No digital (37, 158, 157)-net over F₄	[i]
10	No digital (37, 159, 157)-net over F₄	[i]
11	No digital (37, 160, 157)-net over F₄	[i]
12	No digital (37, 161, 157)-net over F₄	[i]
13	No digital (37, 162, 157)-net over F₄	[i]
14	No digital (37, 163, 157)-net over F₄	[i]
15	No digital (37, 164, 157)-net over F₄	[i]
16	No digital (37, 165, 157)-net over F₄	[i]
17	No digital (37, 166, 157)-net over F₄	[i]
18	No digital (37, 167, 157)-net over F₄	[i]
19	No digital (37, 168, 157)-net over F₄	[i]
20	No digital (37, 169, 157)-net over F₄	[i]
21	No digital (37, 170, 157)-net over F₄	[i]
22	No digital (37, 171, 157)-net over F₄	[i]
23	No digital (37, 172, 157)-net over F₄	[i]
24	No digital (37, 173, 157)-net over F₄	[i]
25	No digital (37, 174, 157)-net over F₄	[i]
26	No digital (37, 175, 157)-net over F₄	[i]
27	No digital (37, 176, 157)-net over F₄	[i]
28	No digital (37, 177, 157)-net over F₄	[i]
29	No digital (37, 178, 157)-net over F₄	[i]
30	No digital (37, 179, 157)-net over F₄	[i]
31	No digital (37, 180, 157)-net over F₄	[i]
32	No digital (37, 181, 157)-net over F₄	[i]
33	No digital (37, 182, 157)-net over F₄	[i]
34	No digital (37, 183, 157)-net over F₄	[i]
35	No digital (37, 184, 157)-net over F₄	[i]
36	No digital (37, 185, 157)-net over F₄	[i]
37	No digital (37, 186, 157)-net over F₄	[i]
38	No digital (37, 187, 157)-net over F₄	[i]
39	No digital (37, 188, 157)-net over F₄	[i]
40	No digital (37, 189, 157)-net over F₄	[i]
41	No digital (37, 190, 157)-net over F₄	[i]
42	No digital (37, 191, 157)-net over F₄	[i]
43	No digital (37, 192, 157)-net over F₄	[i]
44	No digital (37, 193, 157)-net over F₄	[i]
45	No digital (37, 194, 157)-net over F₄	[i]
46	No digital (37, 195, 157)-net over F₄	[i]
47	No digital (37, 196, 157)-net over F₄	[i]
48	No digital (37, 197, 157)-net over F₄	[i]
49	No digital (37, 198, 157)-net over F₄	[i]
50	No digital (37, 199, 157)-net over F₄	[i]
51	No digital (37, 200, 157)-net over F₄	[i]
52	No digital (37, 201, 157)-net over F₄	[i]
53	No digital (37, 202, 157)-net over F₄	[i]
54	No digital (37, 203, 157)-net over F₄	[i]
55	No digital (37, 204, 157)-net over F₄	[i]
56	No digital (37, 205, 157)-net over F₄	[i]
57	No digital (37, 206, 157)-net over F₄	[i]
58	No digital (37, 207, 157)-net over F₄	[i]
59	No digital (37, 208, 157)-net over F₄	[i]
60	No digital (37, 209, 157)-net over F₄	[i]
61	No digital (37, 210, 157)-net over F₄	[i]
62	No digital (37, 211, 157)-net over F₄	[i]
63	No digital (37, 212, 157)-net over F₄	[i]
64	No digital (37, 213, 157)-net over F₄	[i]
65	No digital (37, 214, 157)-net over F₄	[i]
66	No digital (37, 215, 157)-net over F₄	[i]
67	No digital (37, 216, 157)-net over F₄	[i]
68	No digital (37, 217, 157)-net over F₄	[i]
69	No digital (37, 218, 157)-net over F₄	[i]
70	No digital (37, 219, 157)-net over F₄	[i]
71	No digital (37, 220, 157)-net over F₄	[i]
72	No digital (37, 221, 157)-net over F₄	[i]
73	No digital (37, 222, 157)-net over F₄	[i]
74	No digital (37, 223, 157)-net over F₄	[i]
75	No digital (37, 224, 157)-net over F₄	[i]
76	No digital (37, 225, 157)-net over F₄	[i]
77	No digital (37, 226, 157)-net over F₄	[i]
78	No digital (37, 227, 157)-net over F₄	[i]
79	No digital (37, 228, 157)-net over F₄	[i]
80	No digital (37, 229, 157)-net over F₄	[i]
81	No digital (37, 230, 157)-net over F₄	[i]
82	No digital (37, 231, 157)-net over F₄	[i]
83	No digital (37, 232, 157)-net over F₄	[i]
84	No digital (37, 233, 157)-net over F₄	[i]
85	No digital (37, 234, 157)-net over F₄	[i]
86	No digital (37, 235, 157)-net over F₄	[i]
87	No digital (37, 236, 157)-net over F₄	[i]
88	No digital (37, 237, 157)-net over F₄	[i]
89	No digital (37, 238, 157)-net over F₄	[i]
90	No digital (37, 239, 157)-net over F₄	[i]
91	No digital (37, 240, 157)-net over F₄	[i]
92	No digital (37, 241, 157)-net over F₄	[i]
93	No digital (37, 242, 157)-net over F₄	[i]
94	No digital (37, 243, 157)-net over F₄	[i]
95	No digital (37, 244, 157)-net over F₄	[i]
96	No digital (37, 245, 157)-net over F₄	[i]
97	No digital (37, 246, 157)-net over F₄	[i]
98	No digital (37, 247, 157)-net over F₄	[i]
99	No digital (37, 248, 157)-net over F₄	[i]
100	No digital (37, 249, 157)-net over F₄	[i]
101	No digital (37, 250, 157)-net over F₄	[i]
102	No digital (37, 251, 157)-net over F₄	[i]
103	No digital (37, 252, 157)-net over F₄	[i]
104	No digital (37, 253, 157)-net over F₄	[i]
105	No digital (37, 254, 157)-net over F₄	[i]
106	No digital (37, 255, 157)-net over F₄	[i]
107	No digital (37, 256, 157)-net over F₄	[i]
108	No digital (37, 257, 157)-net over F₄	[i]