MinT - Information on Result #1215475

Information on Result #1215475

Digital (147, 163, 2105369)-net over F₈, using (u,Â u+v)-construction based on

digital (33, 41, 8219)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (2, 6, 28)-net over F₈, using
    - net defined by OOA [i] based on linear OOA(8⁶, 28, F₈, 4, 4) (dual of [(28, 4), 106, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(8⁶, 28, F₈, 3, 4) (dual of [(28, 3), 78, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(8⁶, 56, F₈, 4) (dual of [56, 50, 5]-code), using
        1 times truncation [i] based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
        a code by Danev and Olsson [i]
  2. digital (27, 35, 8191)-net over F₈, using
    - net defined by OOA [i] based on linear OOA(8³⁵, 8191, F₈, 8, 8) (dual of [(8191, 8), 65493, 9]-NRT-code), using
      - OA 4-folding and stacking [i] based on linear OA(8³⁵, 32764, F₈, 8) (dual of [32764, 32729, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(8³⁵, 32767, F₈, 8) (dual of [32767, 32732, 9]-code), using
        1 times truncation [i] based on linear OA(8³⁶, 32768, F₈, 9) (dual of [32768, 32732, 10]-code), using
        an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
digital (106, 122, 2097150)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹²², 2097150, F₈, 18, 16) (dual of [(2097150, 18), 37748578, 17]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OOA(8¹²², 8388601, F₈, 2, 16) (dual of [(8388601, 2), 16777080, 17]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹²², 8388602, F₈, 2, 16) (dual of [(8388602, 2), 16777082, 17]-NRT-code), using
      - trace code [i] based on linear OOA(64⁶¹, 4194301, F₆₄, 2, 16) (dual of [(4194301, 2), 8388541, 17]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64⁶¹, 8388602, F₆₄, 16) (dual of [8388602, 8388541, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁶¹, large, F₆₄, 16) (dual of [large, large−61, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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.