Information on Result #599888
There is no digital (16, 120, 254)-net over F9, because extracting embedded orthogonal array would yield linear OA(9120, 254, F9, 104) (dual of [254, 134, 105]-code), but
- construction Y1 [i] would yield
- OA(9119, 137, S9, 104), but
- the linear programming bound shows that M ≥ 1 649743 959172 993378 210906 967412 042627 075594 345401 873516 549288 005769 316925 057707 239007 022709 124331 368314 618099 062045 429872 721572 150117 / 4 003686 893566 937500 > 9119 [i]
- linear OA(9134, 254, F9, 117) (dual of [254, 120, 118]-code), but
- discarding factors / shortening the dual code would yield linear OA(9134, 251, F9, 117) (dual of [251, 117, 118]-code), but
- residual code [i] would yield OA(917, 133, S9, 13), but
- 1 times truncation [i] would yield OA(916, 132, S9, 12), but
- the linear programming bound shows that M ≥ 366759 481988 110308 514537 173543 / 191 274702 307783 > 916 [i]
- 1 times truncation [i] would yield OA(916, 132, S9, 12), but
- residual code [i] would yield OA(917, 133, S9, 13), but
- discarding factors / shortening the dual code would yield linear OA(9134, 251, F9, 117) (dual of [251, 117, 118]-code), but
- OA(9119, 137, S9, 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 (16, 121, 254)-net over F9 | [i] | m-Reduction | |