Information on Result #547860

There is no linear OA(4121, 203, F4, 86) (dual of [203, 82, 87]-code), because construction Y1 would yield
  1. OA(4120, 146, S4, 86), but
    • the linear programming bound shows that M ≥ 1676 785629 901870 831344 687640 931028 998195 565713 094557 086708 745951 276885 969823 837567 017285 582848 / 833 733992 529928 226625 > 4120 [i]
  2. OA(482, 203, S4, 57), but
    • discarding factors would yield OA(482, 147, S4, 57), but
      • the linear programming bound shows that M ≥ 317 037594 874104 788097 363934 385470 033055 949567 295348 251071 808033 395027 252472 917734 505583 665296 587433 584079 322091 728288 179828 060163 502846 553034 526452 257111 175653 922741 542240 051385 314719 039488 / 12 974914 487478 534018 893942 165576 018487 860552 476600 082829 690910 525536 318801 189236 245587 024898 169738 332511 320472 102082 003724 381476 705681 480945 > 482 [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OOA(4121, 203, F4, 2, 86) (dual of [(203, 2), 285, 87]-NRT-code) [i]Depth Reduction
2No linear OOA(4121, 203, F4, 3, 86) (dual of [(203, 3), 488, 87]-NRT-code) [i]
3No digital (35, 121, 203)-net over F4 [i]Extracting Embedded Orthogonal Array