MinT - Information on Result #598886

Information on Result #598886

There is no digital (127, 255, 265)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2²⁵⁵, 265, F₂, 128) (dual of [265, 10, 129]-code), but

residual code [i] 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		Method
1	No digital (127, 256, 265)-net over F₂	[i]	m-Reduction
2	No digital (127, 257, 265)-net over F₂	[i]
3	No digital (127, 258, 265)-net over F₂	[i]
4	No digital (127, 259, 265)-net over F₂	[i]
5	No digital (127, 260, 265)-net over F₂	[i]