MinT - Information on Result #598637

Information on Result #598637

There is no digital (58, 118, 127)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹¹⁸, 127, F₂, 60) (dual of [127, 9, 61]-code), but

residual code [i] would yield linear OA(2⁵⁸, 66, F₂, 30) (dual of [66, 8, 31]-code), but
- adding a parity check bit [i] would yield linear OA(2⁵⁹, 67, F₂, 31) (dual of [67, 8, 32]-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 (58, 119, 127)-net over F₂	[i]		m-Reduction
2	No digital (58, 120, 127)-net over F₂	[i]
3	No digital (58, 121, 127)-net over F₂	[i]
4	No digital (58, 122, 127)-net over F₂	[i]
5	No digital (58, 123, 127)-net over F₂	[i]
6	No digital (58, 124, 127)-net over F₂	[i]
7	No digital (58, 125, 127)-net over F₂	[i]
8	No digital (58, 126, 127)-net over F₂	[i]
9	No digital (58, 127, 127)-net over F₂	[i]
10	No digital (58, 128, 127)-net over F₂	[i]
11	No digital (58, 129, 127)-net over F₂	[i]
12	No digital (58, 130, 127)-net over F₂	[i]
13	No digital (58, 131, 127)-net over F₂	[i]