Information on Result #599573
There is no digital (59, 223, 290)-net over F4, because extracting embedded orthogonal array would yield linear OA(4223, 290, F4, 164) (dual of [290, 67, 165]-code), but
- residual code [i] would yield OA(459, 125, S4, 41), but
- the linear programming bound shows that M ≥ 6 098659 704705 486904 667441 402011 989050 548288 910427 912825 765842 283670 760248 415348 522730 039189 577335 282788 475369 967101 883338 375933 306396 897634 126855 141698 525692 111751 859853 590528 / 17 865783 539531 952003 937094 580988 623442 037272 256331 005047 247373 356459 142621 652981 139301 072409 181322 127802 625025 609129 027701 857126 610015 951793 > 459 [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 (59, 224, 290)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (59, 225, 290)-net over F4 | [i] | ||
| 3 | No digital (59, 226, 290)-net over F4 | [i] | ||