Information on Result #598648
There is no digital (64, 128, 137)-net over F2, because extracting embedded orthogonal array would yield linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), but
- residual code [i] would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
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 (64, 129, 137)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (64, 130, 137)-net over F2 | [i] | ||
| 3 | No digital (64, 131, 137)-net over F2 | [i] | ||
| 4 | No digital (64, 132, 137)-net over F2 | [i] | ||
| 5 | No digital (64, 133, 137)-net over F2 | [i] | ||
| 6 | No digital (64, 134, 137)-net over F2 | [i] | ||
| 7 | No digital (64, 135, 137)-net over F2 | [i] | ||
| 8 | No digital (64, 136, 137)-net over F2 | [i] | ||
| 9 | No digital (64, 137, 137)-net over F2 | [i] | ||
| 10 | No digital (64, 138, 137)-net over F2 | [i] | ||
| 11 | No digital (64, 139, 137)-net over F2 | [i] | ||
| 12 | No digital (64, 140, 137)-net over F2 | [i] | ||
| 13 | No digital (64, 141, 137)-net over F2 | [i] | ||
| 14 | No digital (64, 142, 137)-net over F2 | [i] | ||
| 15 | No digital (64, 143, 137)-net over F2 | [i] | ||
| 16 | No digital (64, 144, 137)-net over F2 | [i] | ||
| 17 | No digital (64, 145, 137)-net over F2 | [i] | ||
| 18 | No digital (64, 146, 137)-net over F2 | [i] | ||
| 19 | No digital (64, 147, 137)-net over F2 | [i] | ||