Information on Result #599563
There is no digital (58, 218, 291)-net over F4, because extracting embedded orthogonal array would yield linear OA(4218, 291, F4, 160) (dual of [291, 73, 161]-code), but
- residual code [i] would yield OA(458, 130, S4, 40), but
- the linear programming bound shows that M ≥ 209544 936299 479389 121518 912044 089753 196453 227215 118049 279760 432327 769939 564811 820879 196123 613172 070974 880613 527842 029138 321043 777447 471353 954304 / 2 470482 844369 173135 750828 733014 583913 640615 187243 459992 006489 938479 554355 225141 791107 956885 358375 430667 629325 > 458 [i]
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 (58, 219, 291)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (58, 220, 291)-net over F4 | [i] | ||
| 3 | No digital (58, 221, 291)-net over F4 | [i] | ||