MinT - Information on Result #598646

Information on Result #598646

There is no digital (63, 127, 136)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹²⁷, 136, F₂, 64) (dual of [136, 9, 65]-code), but

residual code [i] would yield linear OA(2⁶³, 71, F₂, 32) (dual of [71, 8, 33]-code), but
- residual code [i] would yield linear OA(2³¹, 38, F₂, 16) (dual of [38, 7, 17]-code), but
  - residual code [i] would yield linear OA(2¹⁵, 21, F₂, 8) (dual of [21, 6, 9]-code), but
    - residual code [i] would yield linear OA(2⁷, 12, F₂, 4) (dual of [12, 5, 5]-code), but
      - bound by Fontaine and Peterson [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		This result only	Method
1	No digital (63, 128, 136)-net over F₂	[i]		m-Reduction
2	No digital (63, 129, 136)-net over F₂	[i]
3	No digital (63, 130, 136)-net over F₂	[i]
4	No digital (63, 131, 136)-net over F₂	[i]
5	No digital (63, 132, 136)-net over F₂	[i]
6	No digital (63, 133, 136)-net over F₂	[i]
7	No digital (63, 134, 136)-net over F₂	[i]
8	No digital (63, 135, 136)-net over F₂	[i]
9	No digital (63, 136, 136)-net over F₂	[i]
10	No digital (63, 137, 136)-net over F₂	[i]
11	No digital (63, 138, 136)-net over F₂	[i]
12	No digital (63, 139, 136)-net over F₂	[i]
13	No digital (63, 140, 136)-net over F₂	[i]
14	No digital (63, 141, 136)-net over F₂	[i]
15	No digital (63, 142, 136)-net over F₂	[i]