Information on Result #599554
There is no digital (57, 217, 276)-net over F4, because extracting embedded orthogonal array would yield linear OA(4217, 276, F4, 160) (dual of [276, 59, 161]-code), but
- residual code [i] would yield OA(457, 115, S4, 40), but
- the linear programming bound shows that M ≥ 1342 360890 983125 604419 240171 519716 648945 101876 361490 553050 838026 357519 821508 093001 281902 496966 687169 476434 135922 969794 132259 611410 858450 105459 321583 951843 591284 753316 387911 582182 210225 496765 142083 720215 294444 256689 712753 634383 661128 220672 / 62556 178955 518968 237954 851777 165822 720635 469489 559531 576198 945246 246749 285798 445456 187201 128306 946569 457537 344547 604678 005658 660268 156514 242241 855788 497423 435131 135411 095940 105899 895817 042024 977187 310437 > 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, 218, 276)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (57, 219, 276)-net over F4 | [i] | ||
| 3 | No digital (57, 220, 276)-net over F4 | [i] | ||