Information on Result #599662
There is no digital (68, 248, 361)-net over F4, because extracting embedded orthogonal array would yield linear OA(4248, 361, F4, 180) (dual of [361, 113, 181]-code), but
- residual code [i] would yield OA(468, 180, S4, 45), but
- the linear programming bound shows that M ≥ 328494 790735 001198 305199 602445 532392 471737 863161 499929 581656 031112 774235 621273 901469 693549 435944 960000 000000 / 3 747617 146367 023709 191641 153229 380578 240235 288823 915002 005290 401803 > 468 [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 (68, 249, 361)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (68, 250, 361)-net over F4 | [i] | ||
| 3 | No digital (68, 251, 361)-net over F4 | [i] | ||