MinT - Information on Result #599497

Information on Result #599497

There is no digital (49, 197, 205)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁹⁷, 205, F₄, 148) (dual of [205, 8, 149]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁹⁶, 201, F₄, 148) (dual of [201, 5, 149]-code), but
  - residual code [i] would yield linear OA(4⁴⁸, 52, F₄, 37) (dual of [52, 4, 38]-code), but
    - 1 times truncation [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, 205, 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 (49, 198, 205)-net over F₄	[i]	m-Reduction
2	No digital (49, 199, 205)-net over F₄	[i]
3	No digital (49, 200, 205)-net over F₄	[i]
4	No digital (49, 201, 205)-net over F₄	[i]
5	No digital (49, 202, 205)-net over F₄	[i]
6	No digital (49, 203, 205)-net over F₄	[i]
7	No digital (49, 204, 205)-net over F₄	[i]
8	No digital (49, 205, 205)-net over F₄	[i]
9	No digital (49, 206, 205)-net over F₄	[i]
10	No digital (49, 207, 205)-net over F₄	[i]
11	No digital (49, 208, 205)-net over F₄	[i]
12	No digital (49, 209, 205)-net over F₄	[i]
13	No digital (49, 210, 205)-net over F₄	[i]
14	No digital (49, 211, 205)-net over F₄	[i]
15	No digital (49, 212, 205)-net over F₄	[i]
16	No digital (49, 213, 205)-net over F₄	[i]
17	No digital (49, 214, 205)-net over F₄	[i]
18	No digital (49, 215, 205)-net over F₄	[i]
19	No digital (49, 216, 205)-net over F₄	[i]
20	No digital (49, 217, 205)-net over F₄	[i]
21	No digital (49, 218, 205)-net over F₄	[i]
22	No digital (49, 219, 205)-net over F₄	[i]
23	No digital (49, 220, 205)-net over F₄	[i]
24	No digital (49, 221, 205)-net over F₄	[i]
25	No digital (49, 222, 205)-net over F₄	[i]
26	No digital (49, 223, 205)-net over F₄	[i]
27	No digital (49, 224, 205)-net over F₄	[i]
28	No digital (49, 225, 205)-net over F₄	[i]
29	No digital (49, 226, 205)-net over F₄	[i]
30	No digital (49, 227, 205)-net over F₄	[i]
31	No digital (49, 228, 205)-net over F₄	[i]
32	No digital (49, 229, 205)-net over F₄	[i]
33	No digital (49, 230, 205)-net over F₄	[i]
34	No digital (49, 231, 205)-net over F₄	[i]
35	No digital (49, 232, 205)-net over F₄	[i]
36	No digital (49, 233, 205)-net over F₄	[i]
37	No digital (49, 234, 205)-net over F₄	[i]
38	No digital (49, 235, 205)-net over F₄	[i]
39	No digital (49, 236, 205)-net over F₄	[i]
40	No digital (49, 237, 205)-net over F₄	[i]
41	No digital (49, 238, 205)-net over F₄	[i]
42	No digital (49, 239, 205)-net over F₄	[i]
43	No digital (49, 240, 205)-net over F₄	[i]
44	No digital (49, 241, 205)-net over F₄	[i]
45	No digital (49, 242, 205)-net over F₄	[i]
46	No digital (49, 243, 205)-net over F₄	[i]
47	No digital (49, 244, 205)-net over F₄	[i]
48	No digital (49, 245, 205)-net over F₄	[i]
49	No digital (49, 246, 205)-net over F₄	[i]
50	No digital (49, 247, 205)-net over F₄	[i]
51	No digital (49, 248, 205)-net over F₄	[i]
52	No digital (49, 249, 205)-net over F₄	[i]
53	No digital (49, 250, 205)-net over F₄	[i]
54	No digital (49, 251, 205)-net over F₄	[i]
55	No digital (49, 252, 205)-net over F₄	[i]
56	No digital (49, 253, 205)-net over F₄	[i]
57	No digital (49, 254, 205)-net over F₄	[i]
58	No digital (49, 255, 205)-net over F₄	[i]
59	No digital (49, 256, 205)-net over F₄	[i]
60	No digital (49, 257, 205)-net over F₄	[i]
61	No digital (49, 258, 205)-net over F₄	[i]
62	No digital (49, 259, 205)-net over F₄	[i]
63	No digital (49, 260, 205)-net over F₄	[i]