Information on Result #548040
There is no linear OA(1686, 175, F16, 80) (dual of [175, 89, 81]-code), because construction Y1 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
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(1687, 176, F16, 81) (dual of [176, 89, 82]-code) | [i] | Truncation | |
| 2 | No linear OOA(1687, 175, F16, 2, 81) (dual of [(175, 2), 263, 82]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(1688, 175, F16, 2, 82) (dual of [(175, 2), 262, 83]-NRT-code) | [i] | ||
| 4 | No linear OOA(1686, 175, F16, 2, 80) (dual of [(175, 2), 264, 81]-NRT-code) | [i] | Depth Reduction | |
| 5 | No digital (6, 86, 175)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |