Information on Result #599584
There is no digital (60, 228, 289)-net over F4, because extracting embedded orthogonal array would yield linear OA(4228, 289, F4, 168) (dual of [289, 61, 169]-code), but
- residual code [i] would yield OA(460, 120, S4, 42), but
- the linear programming bound shows that M ≥ 290 323585 871668 540958 706283 871420 089371 226973 685105 944092 049613 090277 543017 758174 630279 499647 453693 213959 295987 570365 373495 501567 458190 834202 690982 141368 167162 106346 363122 321383 704967 027230 420318 677240 681705 674259 718795 341724 668084 100666 837764 012913 983488 / 217 009749 131050 124974 338662 159260 162741 593420 668312 475869 644870 983601 362036 477462 521260 959668 929843 611506 134957 195877 747489 996242 167742 452236 130306 867798 356780 551051 603934 664707 901784 404757 406481 175288 812407 108150 526731 > 460 [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 (60, 229, 289)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (60, 230, 289)-net over F4 | [i] | ||
| 3 | No digital (60, 231, 289)-net over F4 | [i] | ||