MinT - Information on Result #599958

Information on Result #599958

There is no digital (1, 53, 56)-net over F₂₇, because extracting embedded orthogonal array would yield linear OA(27⁵³, 56, F₂₇, 52) (dual of [56, 3, 53]-code), but

bound for almost-MDS-codes with dimension nÂ =Â 3 [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 (1, 54, 56)-net over F₂₇	[i]	m-Reduction
2	No digital (1, 55, 56)-net over F₂₇	[i]
3	No digital (1, 56, 56)-net over F₂₇	[i]
4	No digital (1, 57, 56)-net over F₂₇	[i]
5	No digital (1, 58, 56)-net over F₂₇	[i]
6	No digital (1, 59, 56)-net over F₂₇	[i]
7	No digital (1, 60, 56)-net over F₂₇	[i]
8	No digital (1, 61, 56)-net over F₂₇	[i]
9	No digital (1, 62, 56)-net over F₂₇	[i]
10	No digital (1, 63, 56)-net over F₂₇	[i]
11	No digital (1, 64, 56)-net over F₂₇	[i]
12	No digital (1, 65, 56)-net over F₂₇	[i]
13	No digital (1, 66, 56)-net over F₂₇	[i]
14	No digital (1, 67, 56)-net over F₂₇	[i]
15	No digital (1, 68, 56)-net over F₂₇	[i]
16	No digital (1, 69, 56)-net over F₂₇	[i]
17	No digital (1, 70, 56)-net over F₂₇	[i]
18	No digital (1, 71, 56)-net over F₂₇	[i]
19	No digital (1, 72, 56)-net over F₂₇	[i]
20	No digital (1, 73, 56)-net over F₂₇	[i]
21	No digital (1, 74, 56)-net over F₂₇	[i]
22	No digital (1, 75, 56)-net over F₂₇	[i]
23	No digital (1, 76, 56)-net over F₂₇	[i]
24	No digital (1, 77, 56)-net over F₂₇	[i]
25	No digital (1, 78, 56)-net over F₂₇	[i]
26	No digital (1, 79, 56)-net over F₂₇	[i]
27	No digital (1, 80, 56)-net over F₂₇	[i]
28	No digital (1, 81, 56)-net over F₂₇	[i]
29	No digital (1, 82, 56)-net over F₂₇	[i]
30	No digital (1, 83, 56)-net over F₂₇	[i]
31	No digital (1, 84, 56)-net over F₂₇	[i]
32	No digital (1, 85, 56)-net over F₂₇	[i]
33	No digital (1, 86, 56)-net over F₂₇	[i]
34	No digital (1, 87, 56)-net over F₂₇	[i]
35	No digital (1, 88, 56)-net over F₂₇	[i]
36	No digital (1, 89, 56)-net over F₂₇	[i]
37	No digital (1, 90, 56)-net over F₂₇	[i]
38	No digital (1, 91, 56)-net over F₂₇	[i]
39	No digital (1, 92, 56)-net over F₂₇	[i]
40	No digital (1, 93, 56)-net over F₂₇	[i]
41	No digital (1, 94, 56)-net over F₂₇	[i]
42	No digital (1, 95, 56)-net over F₂₇	[i]
43	No digital (1, 96, 56)-net over F₂₇	[i]
44	No digital (1, 97, 56)-net over F₂₇	[i]
45	No digital (1, 98, 56)-net over F₂₇	[i]
46	No digital (1, 99, 56)-net over F₂₇	[i]
47	No digital (1, 100, 56)-net over F₂₇	[i]
48	No digital (1, 101, 56)-net over F₂₇	[i]
49	No digital (1, 102, 56)-net over F₂₇	[i]
50	No digital (1, 103, 56)-net over F₂₇	[i]
51	No digital (1, 104, 56)-net over F₂₇	[i]
52	No digital (1, 105, 56)-net over F₂₇	[i]
53	No digital (1, 106, 56)-net over F₂₇	[i]
54	No digital (1, 107, 56)-net over F₂₇	[i]
55	No digital (1, 108, 56)-net over F₂₇	[i]
56	No digital (1, 109, 56)-net over F₂₇	[i]
57	No digital (1, 110, 56)-net over F₂₇	[i]
58	No digital (1, m, 56)-net over F₂₇ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net