Information on Result #598821
There is no digital (98, 196, 209)-net over F2, because extracting embedded orthogonal array would yield linear OA(2196, 209, F2, 98) (dual of [209, 13, 99]-code), but
- construction Y1 [i] 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
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- residual code [i] would yield linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-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(297, 106, F2, 49) (dual of [106, 9, 50]-code), but
- OA(213, 209, 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(2195, 205, F2, 98) (dual of [205, 10, 99]-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 (98, 197, 209)-net over F2 | [i] | m-Reduction | |