MinT - Information on Result #599716

Information on Result #599716

There is no digital (6, 31, 39)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5³¹, 39, F₅, 25) (dual of [39, 8, 26]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(5³⁰, 33, F₅, 25) (dual of [33, 3, 26]-code), but
  - Griesmer bound [i]
2. OA(5⁸, 39, S₅, 6), but
  - discarding factors would yield OA(5⁸, 34, S₅, 6), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 392089 > 5⁸ [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 (6, 32, 39)-net over F₅	[i]	m-Reduction
2	No digital (6, 33, 39)-net over F₅	[i]
3	No digital (6, 34, 39)-net over F₅	[i]
4	No digital (6, 35, 39)-net over F₅	[i]
5	No digital (6, 36, 39)-net over F₅	[i]
6	No digital (6, 37, 39)-net over F₅	[i]
7	No digital (6, 38, 39)-net over F₅	[i]
8	No digital (6, 39, 39)-net over F₅	[i]
9	No digital (6, 40, 39)-net over F₅	[i]
10	No digital (6, 41, 39)-net over F₅	[i]
11	No digital (6, 42, 39)-net over F₅	[i]
12	No digital (6, 43, 39)-net over F₅	[i]
13	No digital (6, 44, 39)-net over F₅	[i]
14	No digital (6, 45, 39)-net over F₅	[i]
15	No digital (6, 46, 39)-net over F₅	[i]
16	No digital (6, 47, 39)-net over F₅	[i]
17	No digital (6, 48, 39)-net over F₅	[i]
18	No digital (6, 49, 39)-net over F₅	[i]
19	No digital (6, 50, 39)-net over F₅	[i]
20	No digital (6, 51, 39)-net over F₅	[i]
21	No digital (6, 52, 39)-net over F₅	[i]
22	No digital (6, 53, 39)-net over F₅	[i]
23	No digital (6, 54, 39)-net over F₅	[i]
24	No digital (6, 55, 39)-net over F₅	[i]
25	No digital (6, 56, 39)-net over F₅	[i]
26	No digital (6, 57, 39)-net over F₅	[i]
27	No digital (6, 58, 39)-net over F₅	[i]
28	No digital (6, 59, 39)-net over F₅	[i]
29	No digital (6, 60, 39)-net over F₅	[i]
30	No digital (6, 61, 39)-net over F₅	[i]
31	No digital (6, 62, 39)-net over F₅	[i]
32	No digital (6, 63, 39)-net over F₅	[i]
33	No digital (6, 64, 39)-net over F₅	[i]
34	No digital (6, 65, 39)-net over F₅	[i]
35	No digital (6, 66, 39)-net over F₅	[i]
36	No digital (6, 67, 39)-net over F₅	[i]
37	No digital (6, 68, 39)-net over F₅	[i]