Information on Result #598908
There is no digital (136, 246, 386)-net over F2, because extracting embedded orthogonal array would yield linear OA(2246, 386, F2, 110) (dual of [386, 140, 111]-code), but
- construction Y1 [i] would yield
- linear OA(2245, 332, F2, 110) (dual of [332, 87, 111]-code), but
- construction Y1 [i] would yield
- OA(2244, 300, S2, 110), but
- the linear programming bound shows that M ≥ 727209 932038 995964 963694 786156 506719 769259 430085 807852 102717 045283 079365 167115 254635 995296 956416 / 21378 491075 472167 578125 > 2244 [i]
- OA(287, 332, S2, 32), but
- discarding factors would yield OA(287, 302, S2, 32), but
- the Rao or (dual) Hamming bound shows that M ≥ 161 699122 225452 699910 750634 > 287 [i]
- discarding factors would yield OA(287, 302, S2, 32), but
- OA(2244, 300, S2, 110), but
- construction Y1 [i] would yield
- linear OA(2140, 386, F2, 54) (dual of [386, 246, 55]-code), but
- discarding factors / shortening the dual code would yield linear OA(2140, 376, F2, 54) (dual of [376, 236, 55]-code), but
- the improved Johnson bound shows that N ≤ 638271 859848 635367 775356 676031 149307 988937 824926 330314 504342 114737 011555 < 2236 [i]
- discarding factors / shortening the dual code would yield linear OA(2140, 376, F2, 54) (dual of [376, 236, 55]-code), but
- linear OA(2245, 332, F2, 110) (dual of [332, 87, 111]-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 (136, 247, 386)-net over F2 | [i] | m-Reduction | |