Information on Result #548079

There is no linear OA(8107, 236, F8, 91) (dual of [236, 129, 92]-code), because construction Y1 would yield
  1. OA(8106, 126, S8, 91), but
    • the linear programming bound shows that M ≥ 293 187232 858468 601478 195121 704673 897819 671593 603287 520903 422450 275883 600667 509529 168717 037019 908153 862692 395005 509632 / 543 414185 869329 742359 > 8106 [i]
  2. linear OA(8129, 236, F8, 110) (dual of [236, 107, 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(8107, 236, F8, 2, 91) (dual of [(236, 2), 365, 92]-NRT-code) [i]Depth Reduction
2No linear OOA(8107, 236, F8, 3, 91) (dual of [(236, 3), 601, 92]-NRT-code) [i]
3No digital (16, 107, 236)-net over F8 [i]Extracting Embedded Orthogonal Array