Information on Result #598853
There is no digital (117, 205, 363)-net over F2, because extracting embedded orthogonal array would yield linear OA(2205, 363, F2, 88) (dual of [363, 158, 89]-code), but
- construction Y1 [i] would yield
- OA(2204, 299, S2, 88), but
- adding a parity check bit [i] would yield OA(2205, 300, S2, 89), but
- the linear programming bound shows that M ≥ 416927 463188 475542 795463 940731 898983 181308 104641 213119 598295 609827 594303 154474 074874 094714 331435 368448 / 5584 401256 756961 297780 513782 298869 514125 > 2205 [i]
- adding a parity check bit [i] would yield OA(2205, 300, S2, 89), but
- linear OA(2158, 363, F2, 64) (dual of [363, 205, 65]-code), but
- the improved Johnson bound shows that N ≤ 1214 271568 452769 866939 025066 626311 211727 927188 642255 823141 634304 < 2205 [i]
- OA(2204, 299, S2, 88), 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 (117, 206, 363)-net over F2 | [i] | m-Reduction | |