Information on Result #599680
There is no digital (71, 251, 410)-net over F4, because extracting embedded orthogonal array would yield linear OA(4251, 410, F4, 180) (dual of [410, 159, 181]-code), but
- residual code [i] would yield OA(471, 229, S4, 45), but
- the linear programming bound shows that M ≥ 877 912702 924905 625680 913013 034326 550228 995916 587809 875578 704494 502776 185113 709858 393246 285168 640000 / 155 079140 374101 434134 168939 696571 367080 998053 409783 569671 > 471 [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 (71, 252, 410)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (71, 253, 410)-net over F4 | [i] | ||
| 3 | No digital (71, 254, 410)-net over F4 | [i] | ||