MinT - Information on Result #598626

Information on Result #598626

There is no digital (51, 103, 112)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹⁰³, 112, F₂, 52) (dual of [112, 9, 53]-code), but

residual code [i] would yield linear OA(2⁵¹, 59, F₂, 26) (dual of [59, 8, 27]-code), but
- adding a parity check bit [i] would yield linear OA(2⁵², 60, F₂, 27) (dual of [60, 8, 28]-code), but
  - â€œBJVâ€ 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 (51, 104, 112)-net over F₂	[i]		m-Reduction
2	No digital (51, 105, 112)-net over F₂	[i]
3	No digital (51, 106, 112)-net over F₂	[i]
4	No digital (51, 107, 112)-net over F₂	[i]
5	No digital (51, 108, 112)-net over F₂	[i]
6	No digital (51, 109, 112)-net over F₂	[i]
7	No digital (51, 110, 112)-net over F₂	[i]
8	No digital (51, 111, 112)-net over F₂	[i]
9	No digital (51, 112, 112)-net over F₂	[i]
10	No digital (51, 113, 112)-net over F₂	[i]
11	No digital (51, 114, 112)-net over F₂	[i]
12	No digital (51, 115, 112)-net over F₂	[i]
13	No digital (51, 116, 112)-net over F₂	[i]