MinT - Information on Result #1215130

Information on Result #1215130

Digital (82, 92, 3360057)-net over F₈, using (u,Â u+v)-construction based on

digital (13, 18, 4617)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹⁸, 4617, F₈, 6, 5) (dual of [(4617, 6), 27684, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(8¹⁸, 4618, F₈, 2, 5) (dual of [(4618, 2), 9218, 6]-NRT-code), 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. linear OOA(8¹⁴, 4033, F₈, 2, 5) (dual of [(4033, 2), 8052, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
        trace code [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 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 and linear.

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.