Information on Result #3147829
There is no digital (38, 145, 199)-net over F4, because 3 times m-reduction would yield digital (38, 142, 199)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(4142, 199, F4, 104) (dual of [199, 57, 105]-code), but
- construction Y1 [i] would yield
- linear OA(4141, 163, F4, 104) (dual of [163, 22, 105]-code), but
- construction Y1 [i] would yield
- OA(4140, 151, S4, 104), but
- 2 times truncation [i] would yield OA(4138, 149, S4, 102), but
- the linear programming bound shows that M ≥ 11 769278 720446 703333 267659 747956 551886 187319 922656 933070 157940 129170 842786 675855 465333 653504 / 85 907459 > 4138 [i]
- 2 times truncation [i] would yield OA(4138, 149, S4, 102), but
- OA(422, 163, S4, 12), but
- the linear programming bound shows that M ≥ 22822 886502 605724 057600 / 1273 153051 > 422 [i]
- OA(4140, 151, S4, 104), but
- construction Y1 [i] would yield
- OA(457, 199, S4, 36), but
- discarding factors would yield OA(457, 195, S4, 36), but
- the linear programming bound shows that M ≥ 494 490067 436667 455875 598203 818411 591542 653847 684514 372082 636620 702806 966272 / 22309 972171 916724 959618 830756 395146 773299 > 457 [i]
- discarding factors would yield OA(457, 195, S4, 36), but
- linear OA(4141, 163, F4, 104) (dual of [163, 22, 105]-code), but
- construction Y1 [i] would yield
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
None.