Information on Result #548002

There is no linear OA(8127, 248, F8, 108) (dual of [248, 121, 109]-code), because construction Y1 would yield
  1. OA(8126, 145, S8, 108), but
    • the linear programming bound shows that M ≥ 12 932933 305143 709346 392174 604017 697892 648617 237952 536501 914410 862687 958738 453900 246359 374586 881917 923079 261798 445127 392936 798994 825216 / 15 560886 200942 671875 > 8126 [i]
  2. linear OA(8121, 248, F8, 103) (dual of [248, 127, 104]-code), but
    • discarding factors / shortening the dual code would yield linear OA(8121, 236, F8, 103) (dual of [236, 115, 104]-code), but
      • construction Y1 [i] would yield
        1. OA(8120, 138, S8, 103), but
          • the linear programming bound shows that M ≥ 111645 453241 746255 920862 684222 479803 153865 164146 020446 912158 451311 961713 255226 562612 641032 127218 234498 669820 214273 467205 287936 / 44751 440946 265625 > 8120 [i]
        2. OA(8115, 236, 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(8127, 248, F8, 2, 108) (dual of [(248, 2), 369, 109]-NRT-code) [i]Depth Reduction
2No linear OOA(8127, 248, F8, 3, 108) (dual of [(248, 3), 617, 109]-NRT-code) [i]
3No digital (19, 127, 248)-net over F8 [i]Extracting Embedded Orthogonal Array