MinT - Information on Result #598623

Information on Result #598623

There is no digital (50, 102, 110)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹⁰², 110, F₂, 52) (dual of [110, 8, 53]-code), but

residual code [i] would yield linear OA(2⁵⁰, 57, F₂, 26) (dual of [57, 7, 27]-code), but
- adding a parity check bit [i] would yield linear OA(2⁵¹, 58, F₂, 27) (dual of [58, 7, 28]-code), but
  - â€œvT3â€ 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 (50, 103, 110)-net over F₂	[i]		m-Reduction
2	No digital (50, 104, 110)-net over F₂	[i]
3	No digital (50, 105, 110)-net over F₂	[i]
4	No digital (50, 106, 110)-net over F₂	[i]
5	No digital (50, 107, 110)-net over F₂	[i]
6	No digital (50, 108, 110)-net over F₂	[i]
7	No digital (50, 109, 110)-net over F₂	[i]
8	No digital (50, 110, 110)-net over F₂	[i]
9	No digital (50, 111, 110)-net over F₂	[i]
10	No digital (50, 112, 110)-net over F₂	[i]
11	No digital (50, 113, 110)-net over F₂	[i]