Information on Result #599750
There is no digital (30, 130, 192)-net over F5, because extracting embedded orthogonal array would yield linear OA(5130, 192, F5, 100) (dual of [192, 62, 101]-code), but
- construction Y1 [i] would yield
- OA(5129, 148, S5, 100), but
- the linear programming bound shows that M ≥ 437019 493054 884386 993159 269280 163944 474914 010322 994172 449412 913421 078197 284685 984413 954429 328441 619873 046875 / 236583 689197 696731 > 5129 [i]
- OA(562, 192, S5, 44), but
- discarding factors would yield OA(562, 190, S5, 44), but
- the linear programming bound shows that M ≥ 5 531619 630605 621733 791634 558919 444104 118885 526484 067787 791939 510637 894272 804260 253906 250000 000000 000000 / 236416 842360 352611 941840 260955 732881 660879 805306 461094 587839 > 562 [i]
- discarding factors would yield OA(562, 190, S5, 44), but
- OA(5129, 148, S5, 100), 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 (30, 131, 192)-net over F5 | [i] | m-Reduction | |