MinT - Information on Result #598833

Information on Result #598833

There is no digital (102, 206, 215)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2²⁰⁶, 215, F₂, 104) (dual of [215, 9, 105]-code), but

residual code [i] 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		Method
1	No digital (102, 207, 215)-net over F₂	[i]	m-Reduction
2	No digital (102, 208, 215)-net over F₂	[i]
3	No digital (102, 209, 215)-net over F₂	[i]
4	No digital (102, 210, 215)-net over F₂	[i]
5	No digital (102, 211, 215)-net over F₂	[i]
6	No digital (102, 212, 215)-net over F₂	[i]
7	No digital (102, 213, 215)-net over F₂	[i]
8	No digital (102, 214, 215)-net over F₂	[i]
9	No digital (102, 215, 215)-net over F₂	[i]
10	No digital (102, 216, 215)-net over F₂	[i]
11	No digital (102, 217, 215)-net over F₂	[i]
12	No digital (102, 218, 215)-net over F₂	[i]
13	No digital (102, 219, 215)-net over F₂	[i]
14	No digital (102, 220, 215)-net over F₂	[i]
15	No digital (102, 221, 215)-net over F₂	[i]
16	No digital (102, 222, 215)-net over F₂	[i]
17	No digital (102, 223, 215)-net over F₂	[i]
18	No digital (102, 224, 215)-net over F₂	[i]
19	No digital (102, 225, 215)-net over F₂	[i]
20	No digital (102, 226, 215)-net over F₂	[i]
21	No digital (102, 227, 215)-net over F₂	[i]
22	No digital (102, 228, 215)-net over F₂	[i]
23	No digital (102, 229, 215)-net over F₂	[i]