MinT - Information on Result #550325

Information on Result #550325

There is no linear OOA(8¹²⁷, 248, F₈, 2, 108) (dual of [(248, 2), 369, 109]-NRT-code), because 1 times depth reduction would yield linear OA(8¹²⁷, 248, F₈, 108) (dual of [248, 121, 109]-code), but

constructionÂ Y1 [i] would yield
1. OA(8¹²⁶, 145, S₈, 108), but
  - the linear programming bound shows that MÂ â‰¥ 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
    - constructionÂ Y1 [i] would yield
      1. OA(8¹²⁰, 138, S₈, 103), but
        the linear programming bound shows that MÂ â‰¥ 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 MÂ â‰¥ 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

None.