Information on Result #598893
There is no digital (129, 257, 270)-net over F2, because extracting embedded orthogonal array would yield linear OA(2257, 270, F2, 128) (dual of [270, 13, 129]-code), but
- construction Y1 [i] would yield
- linear OA(2256, 266, F2, 128) (dual of [266, 10, 129]-code), but
- residual code [i] 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
- residual code [i] would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- residual code [i] would yield linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), but
- OA(213, 270, S2, 4), but
- discarding factors would yield OA(213, 128, S2, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 8257 > 213 [i]
- discarding factors would yield OA(213, 128, S2, 4), but
- linear OA(2256, 266, F2, 128) (dual of [266, 10, 129]-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 (129, 258, 270)-net over F2 | [i] | m-Reduction | |