Information on Result #599671
There is no digital (69, 257, 350)-net over F4, because extracting embedded orthogonal array would yield linear OA(4257, 350, F4, 188) (dual of [350, 93, 189]-code), but
- residual code [i] would yield OA(469, 161, S4, 47), but
- 1 times truncation [i] would yield OA(468, 160, S4, 46), but
- the linear programming bound shows that M ≥ 10178 629433 929836 486543 068800 140163 269042 043780 022134 664338 507769 510819 622533 364638 543087 235674 689592 586232 641534 482804 572425 994198 736437 248000 / 113203 572801 045878 145860 058818 437218 882917 411800 440768 742206 357256 206420 022337 868833 760142 804084 942919 > 468 [i]
- 1 times truncation [i] would yield OA(468, 160, S4, 46), 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 (69, 258, 350)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (69, 259, 350)-net over F4 | [i] | ||
| 3 | No digital (69, 260, 350)-net over F4 | [i] | ||