MinT - Information on Result #599728

Information on Result #599728

There is no digital (10, 50, 59)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5⁵⁰, 59, F₅, 40) (dual of [59, 9, 41]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(5⁴⁹, 53, F₅, 40) (dual of [53, 4, 41]-code), but
  - residual code [i] would yield linear OA(5⁹, 12, F₅, 8) (dual of [12, 3, 9]-code), but
    - bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
2. OA(5⁹, 59, S₅, 6), but
  - discarding factors would yield OA(5⁹, 58, S₅, 6), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 2 001465 > 5⁹ [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 (10, 51, 59)-net over F₅	[i]	m-Reduction
2	No digital (10, 52, 59)-net over F₅	[i]
3	No digital (10, 53, 59)-net over F₅	[i]
4	No digital (10, 54, 59)-net over F₅	[i]
5	No digital (10, 55, 59)-net over F₅	[i]
6	No digital (10, 56, 59)-net over F₅	[i]
7	No digital (10, 57, 59)-net over F₅	[i]
8	No digital (10, 58, 59)-net over F₅	[i]
9	No digital (10, 59, 59)-net over F₅	[i]
10	No digital (10, 60, 59)-net over F₅	[i]
11	No digital (10, 61, 59)-net over F₅	[i]
12	No digital (10, 62, 59)-net over F₅	[i]
13	No digital (10, 63, 59)-net over F₅	[i]
14	No digital (10, 64, 59)-net over F₅	[i]
15	No digital (10, 65, 59)-net over F₅	[i]
16	No digital (10, 66, 59)-net over F₅	[i]
17	No digital (10, 67, 59)-net over F₅	[i]
18	No digital (10, 68, 59)-net over F₅	[i]
19	No digital (10, 69, 59)-net over F₅	[i]
20	No digital (10, 70, 59)-net over F₅	[i]
21	No digital (10, 71, 59)-net over F₅	[i]
22	No digital (10, 72, 59)-net over F₅	[i]
23	No digital (10, 73, 59)-net over F₅	[i]
24	No digital (10, 74, 59)-net over F₅	[i]
25	No digital (10, 75, 59)-net over F₅	[i]
26	No digital (10, 76, 59)-net over F₅	[i]
27	No digital (10, 77, 59)-net over F₅	[i]
28	No digital (10, 78, 59)-net over F₅	[i]
29	No digital (10, 79, 59)-net over F₅	[i]
30	No digital (10, 80, 59)-net over F₅	[i]
31	No digital (10, 81, 59)-net over F₅	[i]
32	No digital (10, 82, 59)-net over F₅	[i]
33	No digital (10, 83, 59)-net over F₅	[i]
34	No digital (10, 84, 59)-net over F₅	[i]
35	No digital (10, 85, 59)-net over F₅	[i]
36	No digital (10, 86, 59)-net over F₅	[i]
37	No digital (10, 87, 59)-net over F₅	[i]
38	No digital (10, 88, 59)-net over F₅	[i]
39	No digital (10, 89, 59)-net over F₅	[i]
40	No digital (10, 90, 59)-net over F₅	[i]
41	No digital (10, 91, 59)-net over F₅	[i]
42	No digital (10, 92, 59)-net over F₅	[i]
43	No digital (10, 93, 59)-net over F₅	[i]
44	No digital (10, 94, 59)-net over F₅	[i]
45	No digital (10, 95, 59)-net over F₅	[i]
46	No digital (10, 96, 59)-net over F₅	[i]
47	No digital (10, 97, 59)-net over F₅	[i]
48	No digital (10, 98, 59)-net over F₅	[i]
49	No digital (10, 99, 59)-net over F₅	[i]
50	No digital (10, 100, 59)-net over F₅	[i]
51	No digital (10, 101, 59)-net over F₅	[i]
52	No digital (10, 102, 59)-net over F₅	[i]
53	No digital (10, 103, 59)-net over F₅	[i]
54	No digital (10, 104, 59)-net over F₅	[i]