MinT - Information on Result #1842339

Information on Result #1842339

(87, 97, 3421305)-net in base 8, using (u,Â u+v)-construction based on

(18, 23, 65865)-net in base 8, using
- net defined by OOA [i] based on OOA(8²³, 65865, S₈, 6, 5), using
  - OOA stacking with additional row [i] based on OOA(8²³, 65866, S₈, 2, 5), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(8⁴, 585, F₈, 2, 2) (dual of [(585, 2), 1166, 3]-NRT-code), using
        appending kth column [i] based on linear OA(8⁴, 585, F₈, 2) (dual of [585, 581, 3]-code), using
        Hamming code H(4,8) [i]
      2. OOA(8¹⁹, 65281, S₈, 2, 5), using
        OOA 2-folding [i] based on OA(8¹⁹, 130562, S₈, 5), using
        discarding parts of the base [i] based on linear OA(16¹⁴, 130562, F₁₆, 5) (dual of [130562, 130548, 6]-code), using
        trace code [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
digital (64, 74, 3355440)-net over F₈, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64³⁷, 1677720, F₆₄, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
    - OA 5-folding and stacking [i] based on linear OA(64³⁷, 8388600, F₆₄, 10) (dual of [8388600, 8388563, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.