Information on Result #523466
There is no (18, 104, 298)-net in base 8, because extracting embedded orthogonal array would yield OA(8104, 298, S8, 86), but
- 2 times code embedding in larger space [i] would yield OA(8106, 300, S8, 86), but
- the linear programming bound shows that M ≥ 1 813677 875369 152272 942573 621196 635803 751018 569122 832333 904547 616932 539570 207271 570162 414270 186689 351457 296081 136706 550412 470642 195703 863438 843196 001370 665838 185358 641792 018172 364679 217484 628335 048624 343807 042717 307486 862460 898668 811055 605083 015058 362771 936907 178369 827768 336619 556421 972934 712366 195270 776938 420836 098170 782223 082681 191215 701147 981866 592385 175258 023020 676383 298813 952000 / 2 609523 090828 280360 399673 517605 921202 027302 398919 728637 474815 813018 035055 667380 402821 337345 325099 601925 819413 791707 710882 570618 298161 573338 933318 342533 235415 899785 945735 478446 574545 152392 020552 468875 081370 574983 328005 680478 033720 175186 826334 000457 530734 946272 661810 404405 406720 334371 309973 > 8106 [i]
Mode: Bound.
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 (18, 105, 298)-net in base 8 | [i] | m-Reduction | |
| 2 | No (18, 106, 298)-net in base 8 | [i] | ||
| 3 | No (18, 107, 298)-net in base 8 | [i] | ||
| 4 | No (18, 108, 298)-net in base 8 | [i] | ||
| 5 | No (18, 109, 298)-net in base 8 | [i] | ||