Information on Result #599525
There is no digital (54, 202, 278)-net over F4, because extracting embedded orthogonal array would yield linear OA(4202, 278, F4, 148) (dual of [278, 76, 149]-code), but
- residual code [i] would yield OA(454, 129, S4, 37), but
- the linear programming bound shows that M ≥ 109 951098 397829 332336 284728 003022 152431 672399 031028 523197 768001 879521 814905 484058 086588 022784 000000 / 328974 594178 269164 864154 562133 043701 895580 669743 951599 524746 631921 > 454 [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 (54, 203, 278)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (54, 204, 278)-net over F4 | [i] | ||
| 3 | No digital (54, 205, 278)-net over F4 | [i] | ||