MinT - Information on Result #599383

Information on Result #599383

There is no digital (16, 68, 73)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4⁶⁸, 73, F₄, 52) (dual of [73, 5, 53]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4⁶⁷, 70, F₄, 52) (dual of [70, 3, 53]-code), but
  - Griesmer bound [i]
2. linear OA(4⁵, 73, F₄, 3) (dual of [73, 68, 4]-code or 73-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 (16, 69, 73)-net over F₄	[i]	m-Reduction
2	No digital (16, 70, 73)-net over F₄	[i]
3	No digital (16, 71, 73)-net over F₄	[i]
4	No digital (16, 72, 73)-net over F₄	[i]
5	No digital (16, 73, 73)-net over F₄	[i]
6	No digital (16, 74, 73)-net over F₄	[i]
7	No digital (16, 75, 73)-net over F₄	[i]
8	No digital (16, 76, 73)-net over F₄	[i]
9	No digital (16, 77, 73)-net over F₄	[i]
10	No digital (16, 78, 73)-net over F₄	[i]
11	No digital (16, 79, 73)-net over F₄	[i]
12	No digital (16, 80, 73)-net over F₄	[i]
13	No digital (16, 81, 73)-net over F₄	[i]
14	No digital (16, 82, 73)-net over F₄	[i]
15	No digital (16, 83, 73)-net over F₄	[i]
16	No digital (16, 84, 73)-net over F₄	[i]
17	No digital (16, 85, 73)-net over F₄	[i]
18	No digital (16, 86, 73)-net over F₄	[i]
19	No digital (16, 87, 73)-net over F₄	[i]
20	No digital (16, 88, 73)-net over F₄	[i]
21	No digital (16, 89, 73)-net over F₄	[i]
22	No digital (16, 90, 73)-net over F₄	[i]
23	No digital (16, 91, 73)-net over F₄	[i]
24	No digital (16, 92, 73)-net over F₄	[i]
25	No digital (16, 93, 73)-net over F₄	[i]
26	No digital (16, 94, 73)-net over F₄	[i]
27	No digital (16, 95, 73)-net over F₄	[i]
28	No digital (16, 96, 73)-net over F₄	[i]
29	No digital (16, 97, 73)-net over F₄	[i]
30	No digital (16, 98, 73)-net over F₄	[i]
31	No digital (16, 99, 73)-net over F₄	[i]
32	No digital (16, 100, 73)-net over F₄	[i]
33	No digital (16, 101, 73)-net over F₄	[i]
34	No digital (16, 102, 73)-net over F₄	[i]
35	No digital (16, 103, 73)-net over F₄	[i]
36	No digital (16, 104, 73)-net over F₄	[i]
37	No digital (16, 105, 73)-net over F₄	[i]
38	No digital (16, 106, 73)-net over F₄	[i]
39	No digital (16, 107, 73)-net over F₄	[i]
40	No digital (16, 108, 73)-net over F₄	[i]
41	No digital (16, 109, 73)-net over F₄	[i]
42	No digital (16, 110, 73)-net over F₄	[i]
43	No digital (16, 111, 73)-net over F₄	[i]
44	No digital (16, 112, 73)-net over F₄	[i]
45	No digital (16, 113, 73)-net over F₄	[i]
46	No digital (16, 114, 73)-net over F₄	[i]
47	No digital (16, 115, 73)-net over F₄	[i]
48	No digital (16, 116, 73)-net over F₄	[i]
49	No digital (16, 117, 73)-net over F₄	[i]
50	No digital (16, 118, 73)-net over F₄	[i]
51	No digital (16, 119, 73)-net over F₄	[i]
52	No digital (16, 120, 73)-net over F₄	[i]