MinT - Information on Result #550216

Information on Result #550216

There is no linear OOA(5¹¹², 252, F₅, 2, 85) (dual of [(252, 2), 392, 86]-NRT-code), because 1 times depth reduction would yield linear OA(5¹¹², 252, F₅, 85) (dual of [252, 140, 86]-code), but

constructionÂ Y1 [i] would yield
1. OA(5¹¹¹, 143, S₅, 85), but
  - the linear programming bound shows that MÂ â‰¥ 220 445839 236062 243251 966630 886846 194373 438661 017264 989094 781670 909972 692840 028685 168363 153934 478759 765625 / 378 761134 914432 479453 277033 > 5¹¹¹ [i]
2. linear OA(5¹⁴⁰, 252, F₅, 109) (dual of [252, 112, 110]-code), but
  - discarding factors / shortening the dual code would yield linear OA(5¹⁴⁰, 239, F₅, 109) (dual of [239, 99, 110]-code), but
    - constructionÂ Y1 [i] would yield
      1. linear OA(5¹³⁹, 164, F₅, 109) (dual of [164, 25, 110]-code), but
        constructionÂ Y1 [i] would yield
        OA(5¹³⁸, 148, S₅, 109), but
        the linear programming bound shows that MÂ â‰¥ 86 158555 819318 512642 331328 682663 835348 540649 443889 196923 328992 021307 026760 723601 910285 651683 807373 046875 / 29 425011 > 5¹³⁸ [i]
        OA(5²⁵, 164, S₅, 16), but
        discarding factors would yield OA(5²⁵, 148, S₅, 16), but
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 313081 833470 800945 > 5²⁵ [i]
      2. OA(5⁹⁹, 239, S₅, 75), but
        discarding factors would yield OA(5⁹⁹, 147, S₅, 75), but
        the linear programming bound shows that MÂ â‰¥ 10 465163 072971 841494 226679 044239 098519 996159 375872 949750 717770 995481 826038 130942 490580 153891 865933 246663 189493 119716 644287 109375 / 6623 020670 394833 160024 516013 529216 797975 034523 571498 254336 > 5⁹⁹ [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.