Information on Result #599553
There is no digital (57, 213, 291)-net over F4, because extracting embedded orthogonal array would yield linear OA(4213, 291, F4, 156) (dual of [291, 78, 157]-code), but
- residual code [i] would yield OA(457, 134, S4, 39), but
- the linear programming bound shows that M ≥ 2118 872152 947773 735205 614860 840104 993723 173522 547123 836257 668222 520389 144284 698869 497944 229365 678080 000000 / 96823 132929 101376 060431 157559 643789 049324 330608 249156 649224 680559 609039 > 457 [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 (57, 214, 291)-net over F4 | [i] | m-Reduction | |
2 | No digital (57, 215, 291)-net over F4 | [i] | ||
3 | No digital (57, 216, 291)-net over F4 | [i] |