MinT - Information on Result #598815

Information on Result #598815

There is no digital (97, 195, 205)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹⁹⁵, 205, F₂, 98) (dual of [205, 10, 99]-code), but

residual code [i] would yield linear OA(2⁹⁷, 106, F₂, 49) (dual of [106, 9, 50]-code), but
- 1 times truncation [i] would yield linear OA(2⁹⁶, 105, F₂, 48) (dual of [105, 9, 49]-code), but
  - residual code [i] would yield linear OA(2⁴⁸, 56, F₂, 24) (dual of [56, 8, 25]-code), but
    - adding a parity check bit [i] would yield linear OA(2⁴⁹, 57, F₂, 25) (dual of [57, 8, 26]-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		Method
1	No digital (97, 196, 205)-net over F₂	[i]	m-Reduction
2	No digital (97, 197, 205)-net over F₂	[i]
3	No digital (97, 198, 205)-net over F₂	[i]
4	No digital (97, 199, 205)-net over F₂	[i]
5	No digital (97, 200, 205)-net over F₂	[i]
6	No digital (97, 201, 205)-net over F₂	[i]
7	No digital (97, 202, 205)-net over F₂	[i]
8	No digital (97, 203, 205)-net over F₂	[i]
9	No digital (97, 204, 205)-net over F₂	[i]
10	No digital (97, 205, 205)-net over F₂	[i]
11	No digital (97, 206, 205)-net over F₂	[i]
12	No digital (97, 207, 205)-net over F₂	[i]
13	No digital (97, 208, 205)-net over F₂	[i]
14	No digital (97, 209, 205)-net over F₂	[i]
15	No digital (97, 210, 205)-net over F₂	[i]
16	No digital (97, 211, 205)-net over F₂	[i]
17	No digital (97, 212, 205)-net over F₂	[i]
18	No digital (97, 213, 205)-net over F₂	[i]
19	No digital (97, 214, 205)-net over F₂	[i]
20	No digital (97, 215, 205)-net over F₂	[i]
21	No digital (97, 216, 205)-net over F₂	[i]
22	No digital (97, 217, 205)-net over F₂	[i]
23	No digital (97, 218, 205)-net over F₂	[i]