Information on Result #548003

There is no linear OA(8128, 243, F8, 109) (dual of [243, 115, 110]-code), because construction Y1 would yield
  1. OA(8127, 145, S8, 109), but
    • the linear programming bound shows that M ≥ 370787 816966 249062 852393 610324 731218 464642 981958 214207 589442 761157 047942 887269 300626 078793 969256 849590 703514 597288 403035 383113 187328 / 72122 148180 697725 > 8127 [i]
  2. OA(8115, 243, S8, 98), but
    • discarding factors would yield OA(8115, 147, S8, 98), but
      • the linear programming bound shows that M ≥ 599345 416299 388973 235507 022177 177118 046850 911577 140306 689015 460811 889080 427692 784047 046445 821063 607212 795117 279723 192210 808892 966020 579328 / 7743 507384 508665 125912 260586 578125 > 8115 [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OOA(8128, 243, F8, 2, 109) (dual of [(243, 2), 358, 110]-NRT-code) [i]Depth Reduction
2No linear OOA(8128, 243, F8, 3, 109) (dual of [(243, 3), 601, 110]-NRT-code) [i]
3No digital (19, 128, 243)-net over F8 [i]Extracting Embedded Orthogonal Array