MinT - Information on Result #599784

Information on Result #599784

There is no digital (5, 35, 45)-net over F₇, because extracting embedded orthogonal array would yield linear OA(7³⁵, 45, F₇, 30) (dual of [45, 10, 31]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(7³⁴, 37, F₇, 30) (dual of [37, 3, 31]-code), but
  - â€œHi4â€ bound on codes from Brouwerâ€™s database [i]
2. linear OA(7¹⁰, 45, F₇, 8) (dual of [45, 35, 9]-code), but
  - discarding factors / shortening the dual code would yield linear OA(7¹⁰, 42, F₇, 8) (dual of [42, 32, 9]-code), but
    - constructionÂ Y1 [i] would yield
      1. linear OA(7⁹, 14, F₇, 8) (dual of [14, 5, 9]-code), but
        â€œMPaâ€ bound on codes from Brouwerâ€™s database [i]
      2. linear OA(7³², 42, F₇, 28) (dual of [42, 10, 29]-code), but
        discarding factors / shortening the dual code would yield linear OA(7³², 38, F₇, 28) (dual of [38, 6, 29]-code), but
        residual code [i] would yield linear OA(7⁴, 9, F₇, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,7)), but
        bound for MDS codes [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 (5, 36, 45)-net over F₇	[i]	m-Reduction
2	No digital (5, 37, 45)-net over F₇	[i]
3	No digital (5, 38, 45)-net over F₇	[i]
4	No digital (5, 39, 45)-net over F₇	[i]
5	No digital (5, 40, 45)-net over F₇	[i]
6	No digital (5, 41, 45)-net over F₇	[i]
7	No digital (5, 42, 45)-net over F₇	[i]
8	No digital (5, 43, 45)-net over F₇	[i]
9	No digital (5, 44, 45)-net over F₇	[i]
10	No digital (5, 45, 45)-net over F₇	[i]
11	No digital (5, 46, 45)-net over F₇	[i]
12	No digital (5, 47, 45)-net over F₇	[i]
13	No digital (5, 48, 45)-net over F₇	[i]
14	No digital (5, 49, 45)-net over F₇	[i]
15	No digital (5, 50, 45)-net over F₇	[i]
16	No digital (5, 51, 45)-net over F₇	[i]
17	No digital (5, 52, 45)-net over F₇	[i]
18	No digital (5, 53, 45)-net over F₇	[i]
19	No digital (5, 54, 45)-net over F₇	[i]
20	No digital (5, 55, 45)-net over F₇	[i]
21	No digital (5, 56, 45)-net over F₇	[i]
22	No digital (5, 57, 45)-net over F₇	[i]
23	No digital (5, 58, 45)-net over F₇	[i]
24	No digital (5, 59, 45)-net over F₇	[i]
25	No digital (5, 60, 45)-net over F₇	[i]
26	No digital (5, 61, 45)-net over F₇	[i]
27	No digital (5, 62, 45)-net over F₇	[i]
28	No digital (5, 63, 45)-net over F₇	[i]
29	No digital (5, 64, 45)-net over F₇	[i]
30	No digital (5, 65, 45)-net over F₇	[i]
31	No digital (5, 66, 45)-net over F₇	[i]
32	No digital (5, 67, 45)-net over F₇	[i]
33	No digital (5, 68, 45)-net over F₇	[i]
34	No digital (5, 69, 45)-net over F₇	[i]
35	No digital (5, 70, 45)-net over F₇	[i]
36	No digital (5, 71, 45)-net over F₇	[i]
37	No digital (5, 72, 45)-net over F₇	[i]
38	No digital (5, 73, 45)-net over F₇	[i]
39	No digital (5, 74, 45)-net over F₇	[i]
40	No digital (5, 75, 45)-net over F₇	[i]
41	No digital (5, 76, 45)-net over F₇	[i]
42	No digital (5, 77, 45)-net over F₇	[i]
43	No digital (5, 78, 45)-net over F₇	[i]
44	No digital (5, 79, 45)-net over F₇	[i]
45	No digital (5, 80, 45)-net over F₇	[i]
46	No digital (5, 81, 45)-net over F₇	[i]
47	No digital (5, 82, 45)-net over F₇	[i]
48	No digital (5, 83, 45)-net over F₇	[i]
49	No digital (5, 84, 45)-net over F₇	[i]
50	No digital (5, 85, 45)-net over F₇	[i]