Information on Result #548042
There is no linear OA(1690, 150, F16, 84) (dual of [150, 60, 85]-code), because construction Y1 would yield
- linear OA(1689, 94, F16, 84) (dual of [94, 5, 85]-code), but
- construction Y1 [i] would yield
- OA(1688, 90, S16, 84), but
- 4 times truncation [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]
- 4 times truncation [i] would yield OA(1684, 86, S16, 80), but
- OA(165, 94, S16, 4), but
- the linear programming bound shows that M ≥ 2179 760128 / 2071 > 165 [i]
- OA(1688, 90, S16, 84), but
- construction Y1 [i] would yield
- OA(1660, 150, S16, 56), but
- discarding factors would yield OA(1660, 147, S16, 56), but
- the linear programming bound shows that M ≥ 939765 966922 797477 814596 181274 291363 410391 878783 132568 319700 182987 088048 908156 194099 962624 995855 466829 447168 / 521248 355323 503233 415469 012835 684063 > 1660 [i]
- discarding factors would yield OA(1660, 147, S16, 56), 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(1691, 151, F16, 85) (dual of [151, 60, 86]-code) | [i] | Truncation | |
| 2 | No linear OOA(1691, 150, F16, 2, 85) (dual of [(150, 2), 209, 86]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(1690, 150, F16, 2, 84) (dual of [(150, 2), 210, 85]-NRT-code) | [i] | Depth Reduction | |
| 4 | No digital (6, 90, 150)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |