MinT - Information on Result #600035

Information on Result #600035

There is no digital (1, 65, 192)-net over F₆₄, because extracting embedded orthogonal array would yield linear OA(64⁶⁵, 192, F₆₄, 64) (dual of [192, 127, 65]-code), but

dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(64¹²⁷, 192, F₆₄, 126) (dual of [192, 65, 127]-code), but
- discarding factors / shortening the dual code would yield linear OA(64¹²⁷, 130, F₆₄, 126) (dual of [130, 3, 127]-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, 66, 192)-net over F₆₄	[i]	m-Reduction
2	No digital (1, 67, 192)-net over F₆₄	[i]
3	No digital (1, 68, 192)-net over F₆₄	[i]
4	No digital (1, 69, 192)-net over F₆₄	[i]
5	No digital (1, 70, 192)-net over F₆₄	[i]
6	No digital (1, 71, 192)-net over F₆₄	[i]
7	No digital (1, 72, 192)-net over F₆₄	[i]
8	No digital (1, 73, 192)-net over F₆₄	[i]
9	No digital (1, 74, 192)-net over F₆₄	[i]
10	No digital (1, 75, 192)-net over F₆₄	[i]
11	No digital (1, 76, 192)-net over F₆₄	[i]
12	No digital (1, 77, 192)-net over F₆₄	[i]
13	No digital (1, 78, 192)-net over F₆₄	[i]
14	No digital (1, 79, 192)-net over F₆₄	[i]
15	No digital (1, 80, 192)-net over F₆₄	[i]
16	No digital (1, 81, 192)-net over F₆₄	[i]
17	No digital (1, 82, 192)-net over F₆₄	[i]
18	No digital (1, 83, 192)-net over F₆₄	[i]
19	No digital (1, 84, 192)-net over F₆₄	[i]
20	No digital (1, 85, 192)-net over F₆₄	[i]
21	No digital (1, 86, 192)-net over F₆₄	[i]
22	No digital (1, 87, 192)-net over F₆₄	[i]
23	No digital (1, 88, 192)-net over F₆₄	[i]
24	No digital (1, 89, 192)-net over F₆₄	[i]
25	No digital (1, 90, 192)-net over F₆₄	[i]
26	No digital (1, 91, 192)-net over F₆₄	[i]