Information on Result #599834
There is no digital (19, 125, 265)-net over F8, because extracting embedded orthogonal array would yield linear OA(8125, 265, F8, 106) (dual of [265, 140, 107]-code), but
- construction Y1 [i] would yield
- OA(8124, 145, S8, 106), but
- the linear programming bound shows that M ≥ 1 342408 141203 687605 592802 609181 013836 865893 869002 996708 967389 151373 449322 112488 044923 320188 176348 763972 521547 313977 170182 155517 558784 / 126 646656 585020 246257 > 8124 [i]
- linear OA(8140, 265, F8, 120) (dual of [265, 125, 121]-code), but
- discarding factors / shortening the dual code would yield linear OA(8140, 260, F8, 120) (dual of [260, 120, 121]-code), but
- residual code [i] would yield OA(820, 139, S8, 15), but
- 1 times truncation [i] would yield OA(819, 138, S8, 14), but
- the linear programming bound shows that M ≥ 411449 038157 955600 826236 928000 / 2 816739 543071 > 819 [i]
- 1 times truncation [i] would yield OA(819, 138, S8, 14), but
- residual code [i] would yield OA(820, 139, S8, 15), but
- discarding factors / shortening the dual code would yield linear OA(8140, 260, F8, 120) (dual of [260, 120, 121]-code), but
- OA(8124, 145, S8, 106), 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 (19, 126, 265)-net over F8 | [i] | m-Reduction | |