MinT - Information on Result #599368

Information on Result #599368

There is no digital (10, 42, 47)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4⁴², 47, F₄, 32) (dual of [47, 5, 33]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4⁴¹, 44, F₄, 32) (dual of [44, 3, 33]-code), but
  - Griesmer bound [i]
2. linear OA(4⁵, 47, F₄, 3) (dual of [47, 42, 4]-code or 47-cap in PG(4,4)), but
  - discarding factors / shortening the dual code would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
    - 41 is the largest size of a cap in PG(4,Â 4) [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, 43, 47)-net over F₄	[i]	m-Reduction
2	No digital (10, 44, 47)-net over F₄	[i]
3	No digital (10, 45, 47)-net over F₄	[i]
4	No digital (10, 46, 47)-net over F₄	[i]
5	No digital (10, 47, 47)-net over F₄	[i]
6	No digital (10, 48, 47)-net over F₄	[i]
7	No digital (10, 49, 47)-net over F₄	[i]
8	No digital (10, 50, 47)-net over F₄	[i]
9	No digital (10, 51, 47)-net over F₄	[i]
10	No digital (10, 52, 47)-net over F₄	[i]
11	No digital (10, 53, 47)-net over F₄	[i]
12	No digital (10, 54, 47)-net over F₄	[i]
13	No digital (10, 55, 47)-net over F₄	[i]
14	No digital (10, 56, 47)-net over F₄	[i]
15	No digital (10, 57, 47)-net over F₄	[i]
16	No digital (10, 58, 47)-net over F₄	[i]
17	No digital (10, 59, 47)-net over F₄	[i]
18	No digital (10, 60, 47)-net over F₄	[i]
19	No digital (10, 61, 47)-net over F₄	[i]
20	No digital (10, 62, 47)-net over F₄	[i]
21	No digital (10, 63, 47)-net over F₄	[i]
22	No digital (10, 64, 47)-net over F₄	[i]
23	No digital (10, 65, 47)-net over F₄	[i]
24	No digital (10, 66, 47)-net over F₄	[i]
25	No digital (10, 67, 47)-net over F₄	[i]
26	No digital (10, 68, 47)-net over F₄	[i]
27	No digital (10, 69, 47)-net over F₄	[i]
28	No digital (10, 70, 47)-net over F₄	[i]
29	No digital (10, 71, 47)-net over F₄	[i]
30	No digital (10, 72, 47)-net over F₄	[i]
31	No digital (10, 73, 47)-net over F₄	[i]
32	No digital (10, 74, 47)-net over F₄	[i]
33	No digital (10, 75, 47)-net over F₄	[i]
34	No digital (10, 76, 47)-net over F₄	[i]
35	No digital (10, 77, 47)-net over F₄	[i]
36	No digital (10, 78, 47)-net over F₄	[i]
37	No digital (10, 79, 47)-net over F₄	[i]
38	No digital (10, 80, 47)-net over F₄	[i]