Information on Result #599046
There is no digital (52, 145, 216)-net over F3, because extracting embedded orthogonal array would yield linear OA(3145, 216, F3, 93) (dual of [216, 71, 94]-code), but
- residual code [i] would yield OA(352, 122, S3, 31), but
- the linear programming bound shows that M ≥ 19725 986797 755777 852323 435596 460479 202036 641392 776622 387026 170595 661601 866699 763499 067224 083319 101071 843283 443846 889719 591360 / 2985 345408 219380 711117 519513 518083 267277 757151 882703 066172 010819 020295 476643 056764 180222 169772 636319 > 352 [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 (52, 146, 216)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (52, 147, 216)-net over F3 | [i] | ||