Information on Result #598880
There is no digital (126, 224, 348)-net over F2, because extracting embedded orthogonal array would yield linear OA(2224, 348, F2, 98) (dual of [348, 124, 99]-code), but
- construction Y1 [i] would yield
- OA(2223, 300, S2, 98), but
- the linear programming bound shows that M ≥ 1 797227 776840 883681 896516 291018 079602 556004 736527 384481 376471 307374 972535 986485 205069 933364 379648 / 112622 624143 760877 566730 935625 > 2223 [i]
- linear OA(2124, 348, F2, 48) (dual of [348, 224, 49]-code), but
- discarding factors / shortening the dual code would yield linear OA(2124, 332, F2, 48) (dual of [332, 208, 49]-code), but
- the improved Johnson bound shows that N ≤ 1985 666223 770950 387579 854572 849250 190195 414082 522040 623254 891664 < 2208 [i]
- discarding factors / shortening the dual code would yield linear OA(2124, 332, F2, 48) (dual of [332, 208, 49]-code), but
- OA(2223, 300, S2, 98), 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 (126, 225, 348)-net over F2 | [i] | m-Reduction | |