Information on Result #548080

There is no linear OA(8114, 243, F8, 97) (dual of [243, 129, 98]-code), because construction Y1 would yield
  1. OA(8113, 133, S8, 97), but
    • the linear programming bound shows that M ≥ 12 390882 077619 361809 374608 876210 720807 026167 766516 794505 907066 021724 648856 397281 926521 911401 767561 061604 125143 861641 084928 / 10 910069 338930 636875 > 8113 [i]
  2. linear OA(8129, 243, F8, 110) (dual of [243, 114, 111]-code), but
    • discarding factors / shortening the dual code would yield linear OA(8129, 230, F8, 110) (dual of [230, 101, 111]-code), but
      • construction Y1 [i] would yield
        1. OA(8128, 144, S8, 110), but
          • the linear programming bound shows that M ≥ 6109 893966 434273 613815 828543 318095 703793 603744 881950 919851 825987 742070 359262 466307 770153 217353 472069 496822 008994 926770 763501 404160 / 124 535855 141787 > 8128 [i]
        2. OA(8101, 230, S8, 86), but
          • discarding factors would yield OA(8101, 146, S8, 86), but
            • the linear programming bound shows that M ≥ 47452 756982 762840 644180 785646 906838 805374 098587 752364 011747 551574 239635 502216 492748 447610 784265 998302 557863 887131 929643 838881 370395 949171 355783 528448 / 2798 356661 117080 828757 255676 140575 034437 993397 485091 746485 > 8101 [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(8114, 243, F8, 2, 97) (dual of [(243, 2), 372, 98]-NRT-code) [i]Depth Reduction
2No linear OOA(8114, 243, F8, 3, 97) (dual of [(243, 3), 615, 98]-NRT-code) [i]
3No digital (17, 114, 243)-net over F8 [i]Extracting Embedded Orthogonal Array