MinT - Information on Result #598692

Information on Result #598692

There is no digital (74, 150, 159)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹⁵⁰, 159, F₂, 76) (dual of [159, 9, 77]-code), but

residual code [i] would yield linear OA(2⁷⁴, 82, F₂, 38) (dual of [82, 8, 39]-code), but
- adding a parity check bit [i] would yield linear OA(2⁷⁵, 83, F₂, 39) (dual of [83, 8, 40]-code), but
  - â€œDHMâ€ bound on codes from Brouwerâ€™s database [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 (74, 151, 159)-net over F₂	[i]		m-Reduction
2	No digital (74, 152, 159)-net over F₂	[i]
3	No digital (74, 153, 159)-net over F₂	[i]
4	No digital (74, 154, 159)-net over F₂	[i]
5	No digital (74, 155, 159)-net over F₂	[i]
6	No digital (74, 156, 159)-net over F₂	[i]
7	No digital (74, 157, 159)-net over F₂	[i]
8	No digital (74, 158, 159)-net over F₂	[i]
9	No digital (74, 159, 159)-net over F₂	[i]
10	No digital (74, 160, 159)-net over F₂	[i]
11	No digital (74, 161, 159)-net over F₂	[i]
12	No digital (74, 162, 159)-net over F₂	[i]
13	No digital (74, 163, 159)-net over F₂	[i]
14	No digital (74, 164, 159)-net over F₂	[i]
15	No digital (74, 165, 159)-net over F₂	[i]
16	No digital (74, 166, 159)-net over F₂	[i]
17	No digital (74, 167, 159)-net over F₂	[i]