Information on Result #599564
There is no digital (58, 222, 275)-net over F4, because extracting embedded orthogonal array would yield linear OA(4222, 275, F4, 164) (dual of [275, 53, 165]-code), but
- residual code [i] would yield OA(458, 110, S4, 41), but
- the linear programming bound shows that M ≥ 1232 155961 216230 168086 977678 056475 191089 409710 805770 829825 897828 417067 677196 009558 961106 027628 461497 995772 222254 044023 160230 949557 990006 504845 840607 997118 369373 847851 273455 403008 / 13446 810158 281327 760184 995983 919490 800441 646762 168115 151101 794360 608708 987818 154852 821096 884734 101312 394526 499211 581201 357552 019470 400051 102575 > 458 [i]
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 (58, 223, 275)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (58, 224, 275)-net over F4 | [i] | ||
| 3 | No digital (58, 225, 275)-net over F4 | [i] | ||