MinT - Information on Result #598753

Information on Result #598753

There is no digital (85, 173, 182)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹⁷³, 182, F₂, 88) (dual of [182, 9, 89]-code), but

residual code [i] would yield linear OA(2⁸⁵, 93, F₂, 44) (dual of [93, 8, 45]-code), but
- residual code [i] would yield linear OA(2⁴¹, 48, F₂, 22) (dual of [48, 7, 23]-code), but
  - residual code [i] would yield linear OA(2¹⁹, 25, F₂, 11) (dual of [25, 6, 12]-code), but
    - 1 times truncation [i] would yield linear OA(2¹⁸, 24, F₂, 10) (dual of [24, 6, 11]-code), but
      - residual code [i] would yield linear OA(2⁸, 13, F₂, 5) (dual of [13, 5, 6]-code), but
        1 times truncation [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 (85, 174, 182)-net over F₂	[i]	m-Reduction
2	No digital (85, 175, 182)-net over F₂	[i]
3	No digital (85, 176, 182)-net over F₂	[i]
4	No digital (85, 177, 182)-net over F₂	[i]
5	No digital (85, 178, 182)-net over F₂	[i]
6	No digital (85, 179, 182)-net over F₂	[i]
7	No digital (85, 180, 182)-net over F₂	[i]
8	No digital (85, 181, 182)-net over F₂	[i]
9	No digital (85, 182, 182)-net over F₂	[i]
10	No digital (85, 183, 182)-net over F₂	[i]
11	No digital (85, 184, 182)-net over F₂	[i]
12	No digital (85, 185, 182)-net over F₂	[i]
13	No digital (85, 186, 182)-net over F₂	[i]
14	No digital (85, 187, 182)-net over F₂	[i]
15	No digital (85, 188, 182)-net over F₂	[i]
16	No digital (85, 189, 182)-net over F₂	[i]
17	No digital (85, 190, 182)-net over F₂	[i]