Information on Result #598846
There is no digital (107, 205, 267)-net over F2, because extracting embedded orthogonal array would yield linear OA(2205, 267, F2, 98) (dual of [267, 62, 99]-code), but
- construction Y1 [i] would yield
- linear OA(2204, 245, F2, 98) (dual of [245, 41, 99]-code), but
- residual code [i] would yield OA(2106, 146, S2, 49), but
- 1 times truncation [i] would yield OA(2105, 145, S2, 48), but
- the linear programming bound shows that M ≥ 727 070369 678229 731686 401086 929362 121333 407744 / 17 521374 765895 > 2105 [i]
- 1 times truncation [i] would yield OA(2105, 145, S2, 48), but
- residual code [i] would yield OA(2106, 146, S2, 49), but
- OA(262, 267, S2, 22), but
- discarding factors would yield OA(262, 249, S2, 22), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 787396 297110 060300 > 262 [i]
- discarding factors would yield OA(262, 249, S2, 22), but
- linear OA(2204, 245, F2, 98) (dual of [245, 41, 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 (107, 206, 267)-net over F2 | [i] | m-Reduction | |