Information on Result #599466
There is no digital (45, 173, 223)-net over F4, because extracting embedded orthogonal array would yield linear OA(4173, 223, F4, 128) (dual of [223, 50, 129]-code), but
- residual code [i] would yield OA(445, 94, S4, 32), but
- the linear programming bound shows that M ≥ 5620 184626 019067 545133 732595 852193 606492 239172 450795 055293 610024 696241 375244 513537 251173 048636 372484 511737 707886 460600 729196 298240 / 4 490354 977671 109171 977374 825515 463646 543995 191995 384881 187906 235255 501379 117691 433461 827076 002203 266473 > 445 [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 (45, 174, 223)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (45, 175, 223)-net over F4 | [i] | ||
| 3 | No digital (45, 176, 223)-net over F4 | [i] | ||