MinT - Information on Result #599491

Information on Result #599491

There is no digital (48, 192, 200)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁹², 200, F₄, 144) (dual of [200, 8, 145]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁹¹, 196, F₄, 144) (dual of [196, 5, 145]-code), but
  - residual code [i] would yield linear OA(4⁴⁷, 51, F₄, 36) (dual of [51, 4, 37]-code), but
    - a result by Landjev, Maruta, and Hill [i]
2. OA(4⁸, 200, 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 (48, 193, 200)-net over F₄	[i]	m-Reduction
2	No digital (48, 194, 200)-net over F₄	[i]
3	No digital (48, 195, 200)-net over F₄	[i]
4	No digital (48, 196, 200)-net over F₄	[i]
5	No digital (48, 197, 200)-net over F₄	[i]
6	No digital (48, 198, 200)-net over F₄	[i]
7	No digital (48, 199, 200)-net over F₄	[i]
8	No digital (48, 200, 200)-net over F₄	[i]
9	No digital (48, 201, 200)-net over F₄	[i]
10	No digital (48, 202, 200)-net over F₄	[i]
11	No digital (48, 203, 200)-net over F₄	[i]
12	No digital (48, 204, 200)-net over F₄	[i]
13	No digital (48, 205, 200)-net over F₄	[i]
14	No digital (48, 206, 200)-net over F₄	[i]
15	No digital (48, 207, 200)-net over F₄	[i]
16	No digital (48, 208, 200)-net over F₄	[i]
17	No digital (48, 209, 200)-net over F₄	[i]
18	No digital (48, 210, 200)-net over F₄	[i]
19	No digital (48, 211, 200)-net over F₄	[i]
20	No digital (48, 212, 200)-net over F₄	[i]
21	No digital (48, 213, 200)-net over F₄	[i]
22	No digital (48, 214, 200)-net over F₄	[i]
23	No digital (48, 215, 200)-net over F₄	[i]
24	No digital (48, 216, 200)-net over F₄	[i]
25	No digital (48, 217, 200)-net over F₄	[i]
26	No digital (48, 218, 200)-net over F₄	[i]
27	No digital (48, 219, 200)-net over F₄	[i]
28	No digital (48, 220, 200)-net over F₄	[i]
29	No digital (48, 221, 200)-net over F₄	[i]
30	No digital (48, 222, 200)-net over F₄	[i]
31	No digital (48, 223, 200)-net over F₄	[i]
32	No digital (48, 224, 200)-net over F₄	[i]
33	No digital (48, 225, 200)-net over F₄	[i]
34	No digital (48, 226, 200)-net over F₄	[i]
35	No digital (48, 227, 200)-net over F₄	[i]
36	No digital (48, 228, 200)-net over F₄	[i]
37	No digital (48, 229, 200)-net over F₄	[i]
38	No digital (48, 230, 200)-net over F₄	[i]
39	No digital (48, 231, 200)-net over F₄	[i]
40	No digital (48, 232, 200)-net over F₄	[i]
41	No digital (48, 233, 200)-net over F₄	[i]
42	No digital (48, 234, 200)-net over F₄	[i]
43	No digital (48, 235, 200)-net over F₄	[i]
44	No digital (48, 236, 200)-net over F₄	[i]
45	No digital (48, 237, 200)-net over F₄	[i]
46	No digital (48, 238, 200)-net over F₄	[i]
47	No digital (48, 239, 200)-net over F₄	[i]
48	No digital (48, 240, 200)-net over F₄	[i]
49	No digital (48, 241, 200)-net over F₄	[i]
50	No digital (48, 242, 200)-net over F₄	[i]
51	No digital (48, 243, 200)-net over F₄	[i]
52	No digital (48, 244, 200)-net over F₄	[i]
53	No digital (48, 245, 200)-net over F₄	[i]
54	No digital (48, 246, 200)-net over F₄	[i]
55	No digital (48, 247, 200)-net over F₄	[i]
56	No digital (48, 248, 200)-net over F₄	[i]
57	No digital (48, 249, 200)-net over F₄	[i]
58	No digital (48, 250, 200)-net over F₄	[i]
59	No digital (48, 251, 200)-net over F₄	[i]
60	No digital (48, 252, 200)-net over F₄	[i]
61	No digital (48, 253, 200)-net over F₄	[i]
62	No digital (48, 254, 200)-net over F₄	[i]
63	No digital (48, 255, 200)-net over F₄	[i]
64	No digital (48, 256, 200)-net over F₄	[i]
65	No digital (48, 257, 200)-net over F₄	[i]
66	No digital (48, 258, 200)-net over F₄	[i]
67	No digital (48, 259, 200)-net over F₄	[i]
68	No digital (48, 260, 200)-net over F₄	[i]