Information on Result #598857
There is no digital (119, 209, 359)-net over F2, because extracting embedded orthogonal array would yield linear OA(2209, 359, F2, 90) (dual of [359, 150, 91]-code), but
- construction Y1 [i] would yield
- OA(2208, 299, S2, 90), but
- adding a parity check bit [i] would yield OA(2209, 300, S2, 91), but
- the linear programming bound shows that M ≥ 437987 836379 661851 428112 482969 460104 960459 291237 979833 080590 515802 667419 590325 215760 903409 709975 863296 / 433 753365 263741 276278 643266 060465 678125 > 2209 [i]
- adding a parity check bit [i] would yield OA(2209, 300, S2, 91), but
- linear OA(2150, 359, F2, 60) (dual of [359, 209, 61]-code), but
- discarding factors / shortening the dual code would yield linear OA(2150, 354, F2, 60) (dual of [354, 204, 61]-code), but
- the improved Johnson bound shows that N ≤ 570 693273 077464 953259 984159 736256 114541 311702 095039 925212 853150 < 2204 [i]
- discarding factors / shortening the dual code would yield linear OA(2150, 354, F2, 60) (dual of [354, 204, 61]-code), but
- OA(2208, 299, S2, 90), 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 (119, 210, 359)-net over F2 | [i] | m-Reduction | |