Information on Result #599084
There is no digital (57, 162, 217)-net over F3, because extracting embedded orthogonal array would yield linear OA(3162, 217, F3, 105) (dual of [217, 55, 106]-code), but
- residual code [i] would yield OA(357, 111, S3, 35), but
- the linear programming bound shows that M ≥ 37562 646628 132840 923555 510805 524990 698125 854470 702956 611458 206634 330592 972745 571811 693475 463280 794484 310358 798101 613598 520811 498715 852180 394100 485311 718464 678477 379766 250841 111527 263840 998708 126710 102901 010614 878078 058419 / 23 198198 819486 814111 531592 059961 917751 382231 381147 294006 713526 688083 077331 132750 604165 387990 072803 317950 890355 954749 807575 083764 923806 806712 425767 722092 751780 067760 482182 419810 536162 336560 924637 > 357 [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, 163, 217)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (57, 164, 217)-net over F3 | [i] | ||