MinT - Information on Result #599381

Information on Result #599381

There is no digital (15, 63, 68)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4⁶³, 68, F₄, 48) (dual of [68, 5, 49]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4⁶², 65, F₄, 48) (dual of [65, 3, 49]-code), but
  - Griesmer bound [i]
2. linear OA(4⁵, 68, F₄, 3) (dual of [68, 63, 4]-code or 68-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 (15, 64, 68)-net over F₄	[i]	m-Reduction
2	No digital (15, 65, 68)-net over F₄	[i]
3	No digital (15, 66, 68)-net over F₄	[i]
4	No digital (15, 67, 68)-net over F₄	[i]
5	No digital (15, 68, 68)-net over F₄	[i]
6	No digital (15, 69, 68)-net over F₄	[i]
7	No digital (15, 70, 68)-net over F₄	[i]
8	No digital (15, 71, 68)-net over F₄	[i]
9	No digital (15, 72, 68)-net over F₄	[i]
10	No digital (15, 73, 68)-net over F₄	[i]
11	No digital (15, 74, 68)-net over F₄	[i]
12	No digital (15, 75, 68)-net over F₄	[i]
13	No digital (15, 76, 68)-net over F₄	[i]
14	No digital (15, 77, 68)-net over F₄	[i]
15	No digital (15, 78, 68)-net over F₄	[i]
16	No digital (15, 79, 68)-net over F₄	[i]
17	No digital (15, 80, 68)-net over F₄	[i]
18	No digital (15, 81, 68)-net over F₄	[i]
19	No digital (15, 82, 68)-net over F₄	[i]
20	No digital (15, 83, 68)-net over F₄	[i]
21	No digital (15, 84, 68)-net over F₄	[i]
22	No digital (15, 85, 68)-net over F₄	[i]
23	No digital (15, 86, 68)-net over F₄	[i]
24	No digital (15, 87, 68)-net over F₄	[i]
25	No digital (15, 88, 68)-net over F₄	[i]
26	No digital (15, 89, 68)-net over F₄	[i]
27	No digital (15, 90, 68)-net over F₄	[i]
28	No digital (15, 91, 68)-net over F₄	[i]
29	No digital (15, 92, 68)-net over F₄	[i]
30	No digital (15, 93, 68)-net over F₄	[i]
31	No digital (15, 94, 68)-net over F₄	[i]
32	No digital (15, 95, 68)-net over F₄	[i]
33	No digital (15, 96, 68)-net over F₄	[i]
34	No digital (15, 97, 68)-net over F₄	[i]
35	No digital (15, 98, 68)-net over F₄	[i]
36	No digital (15, 99, 68)-net over F₄	[i]
37	No digital (15, 100, 68)-net over F₄	[i]
38	No digital (15, 101, 68)-net over F₄	[i]
39	No digital (15, 102, 68)-net over F₄	[i]
40	No digital (15, 103, 68)-net over F₄	[i]
41	No digital (15, 104, 68)-net over F₄	[i]
42	No digital (15, 105, 68)-net over F₄	[i]
43	No digital (15, 106, 68)-net over F₄	[i]
44	No digital (15, 107, 68)-net over F₄	[i]
45	No digital (15, 108, 68)-net over F₄	[i]
46	No digital (15, 109, 68)-net over F₄	[i]
47	No digital (15, 110, 68)-net over F₄	[i]
48	No digital (15, 111, 68)-net over F₄	[i]
49	No digital (15, 112, 68)-net over F₄	[i]
50	No digital (15, 113, 68)-net over F₄	[i]