Information on Result #598895
There is no digital (130, 234, 332)-net over F2, because extracting embedded orthogonal array would yield linear OA(2234, 332, F2, 104) (dual of [332, 98, 105]-code), but
- construction Y1 [i] would yield
- OA(2233, 296, S2, 104), but
- the linear programming bound shows that M ≥ 40 441027 764911 159411 999678 250893 328460 000589 698723 782371 054222 923004 931887 671319 124733 067264 / 2499 525994 551277 812375 > 2233 [i]
- linear OA(298, 332, F2, 36) (dual of [332, 234, 37]-code), but
- discarding factors / shortening the dual code would yield linear OA(298, 328, F2, 36) (dual of [328, 230, 37]-code), but
- the Johnson bound shows that N ≤ 1638 846907 564815 429866 669910 715625 391366 929534 207151 722672 384476 916602 < 2230 [i]
- discarding factors / shortening the dual code would yield linear OA(298, 328, F2, 36) (dual of [328, 230, 37]-code), but
- OA(2233, 296, S2, 104), 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 (130, 235, 332)-net over F2 | [i] | m-Reduction | |