MinT - Information on Result #599510

Information on Result #599510

There is no digital (51, 207, 215)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4²⁰⁷, 215, F₄, 156) (dual of [215, 8, 157]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4²⁰⁶, 211, F₄, 156) (dual of [211, 5, 157]-code), but
  - residual code [i] would yield linear OA(4⁵⁰, 54, F₄, 39) (dual of [54, 4, 40]-code), but
    - 3 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, 215, 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 (51, 208, 215)-net over F₄	[i]	m-Reduction
2	No digital (51, 209, 215)-net over F₄	[i]
3	No digital (51, 210, 215)-net over F₄	[i]
4	No digital (51, 211, 215)-net over F₄	[i]
5	No digital (51, 212, 215)-net over F₄	[i]
6	No digital (51, 213, 215)-net over F₄	[i]
7	No digital (51, 214, 215)-net over F₄	[i]
8	No digital (51, 215, 215)-net over F₄	[i]
9	No digital (51, 216, 215)-net over F₄	[i]
10	No digital (51, 217, 215)-net over F₄	[i]
11	No digital (51, 218, 215)-net over F₄	[i]
12	No digital (51, 219, 215)-net over F₄	[i]
13	No digital (51, 220, 215)-net over F₄	[i]
14	No digital (51, 221, 215)-net over F₄	[i]
15	No digital (51, 222, 215)-net over F₄	[i]
16	No digital (51, 223, 215)-net over F₄	[i]
17	No digital (51, 224, 215)-net over F₄	[i]
18	No digital (51, 225, 215)-net over F₄	[i]
19	No digital (51, 226, 215)-net over F₄	[i]
20	No digital (51, 227, 215)-net over F₄	[i]
21	No digital (51, 228, 215)-net over F₄	[i]
22	No digital (51, 229, 215)-net over F₄	[i]
23	No digital (51, 230, 215)-net over F₄	[i]
24	No digital (51, 231, 215)-net over F₄	[i]
25	No digital (51, 232, 215)-net over F₄	[i]
26	No digital (51, 233, 215)-net over F₄	[i]
27	No digital (51, 234, 215)-net over F₄	[i]
28	No digital (51, 235, 215)-net over F₄	[i]
29	No digital (51, 236, 215)-net over F₄	[i]
30	No digital (51, 237, 215)-net over F₄	[i]
31	No digital (51, 238, 215)-net over F₄	[i]
32	No digital (51, 239, 215)-net over F₄	[i]
33	No digital (51, 240, 215)-net over F₄	[i]
34	No digital (51, 241, 215)-net over F₄	[i]
35	No digital (51, 242, 215)-net over F₄	[i]
36	No digital (51, 243, 215)-net over F₄	[i]
37	No digital (51, 244, 215)-net over F₄	[i]
38	No digital (51, 245, 215)-net over F₄	[i]
39	No digital (51, 246, 215)-net over F₄	[i]
40	No digital (51, 247, 215)-net over F₄	[i]
41	No digital (51, 248, 215)-net over F₄	[i]
42	No digital (51, 249, 215)-net over F₄	[i]
43	No digital (51, 250, 215)-net over F₄	[i]
44	No digital (51, 251, 215)-net over F₄	[i]
45	No digital (51, 252, 215)-net over F₄	[i]
46	No digital (51, 253, 215)-net over F₄	[i]
47	No digital (51, 254, 215)-net over F₄	[i]
48	No digital (51, 255, 215)-net over F₄	[i]
49	No digital (51, 256, 215)-net over F₄	[i]
50	No digital (51, 257, 215)-net over F₄	[i]
51	No digital (51, 258, 215)-net over F₄	[i]
52	No digital (51, 259, 215)-net over F₄	[i]
53	No digital (51, 260, 215)-net over F₄	[i]