Information on Result #599407
There is no digital (37, 132, 178)-net over F4, because extracting embedded orthogonal array would yield linear OA(4132, 178, F4, 95) (dual of [178, 46, 96]-code), but
- construction Y1 [i] would yield
- OA(4131, 149, S4, 95), but
- the linear programming bound shows that M ≥ 33368 039747 905148 197531 005626 408113 677562 887057 731053 159021 618938 897974 262171 069449 240576 / 3975 943153 > 4131 [i]
- OA(446, 178, S4, 29), but
- discarding factors would yield OA(446, 174, S4, 29), but
- the linear programming bound shows that M ≥ 8506 289708 537907 430011 501124 929257 400094 961052 942336 000000 / 1 703346 550862 338223 360728 253441 > 446 [i]
- discarding factors would yield OA(446, 174, S4, 29), but
- OA(4131, 149, S4, 95), but
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 (37, 133, 178)-net over F4 | [i] | m-Reduction | |