Information on Result #547872
There is no linear OA(4135, 171, F4, 98) (dual of [171, 36, 99]-code), because construction Y1 would yield
- OA(4134, 149, S4, 98), but
- the linear programming bound shows that M ≥ 16 522880 710265 097728 979611 544086 920533 682517 483034 531558 847934 994306 996193 933029 168694 427648 / 26940 869703 > 4134 [i]
- OA(436, 171, S4, 22), but
- discarding factors would yield OA(436, 158, S4, 22), but
- the Rao or (dual) Hamming bound shows that M ≥ 4882 374384 904669 137046 > 436 [i]
- discarding factors would yield OA(436, 158, S4, 22), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(4135, 171, F4, 2, 98) (dual of [(171, 2), 207, 99]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(4135, 171, F4, 3, 98) (dual of [(171, 3), 378, 99]-NRT-code) | [i] | ||
| 3 | No digital (37, 135, 171)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |