Information on Result #599911
There is no digital (6, 86, 175)-net over F16, because extracting embedded orthogonal array would yield linear OA(1686, 175, F16, 80) (dual of [175, 89, 81]-code), but
- construction Y1 [i] would yield
- linear OA(1685, 92, F16, 80) (dual of [92, 7, 81]-code), but
- construction Y1 [i] would yield
- OA(1684, 86, S16, 80), but
- the (dual) Plotkin bound shows that M ≥ 4 479489 484355 608421 114884 561136 888556 243290 994469 299069 799978 201927 583742 360321 890761 754986 543214 231552 / 27 > 1684 [i]
- OA(167, 92, S16, 6), but
- discarding factors would yield OA(167, 80, S16, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 278 002201 > 167 [i]
- discarding factors would yield OA(167, 80, S16, 6), but
- OA(1684, 86, S16, 80), but
- construction Y1 [i] would yield
- OA(1689, 175, S16, 83), but
- discarding factors would yield OA(1689, 165, S16, 83), but
- the linear programming bound shows that M ≥ 15352 684767 685611 086882 809761 984160 188561 571509 004484 738285 092713 831920 008077 971129 525920 055364 921813 182353 415776 911815 913281 106245 860502 560348 270257 729557 233664 / 103836 312412 686023 017550 716368 186316 554556 371946 618739 > 1689 [i]
- discarding factors would yield OA(1689, 165, S16, 83), but
- linear OA(1685, 92, F16, 80) (dual of [92, 7, 81]-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 (6, 87, 175)-net over F16 | [i] | m-Reduction | |
| 2 | No digital (6, 88, 175)-net over F16 | [i] | ||