MinT - Information on Result #1215661

Information on Result #1215661

Digital (145, 165, 1677734)-net over F₈, using (u,Â u+v)-construction based on

digital (1, 11, 14)-net over F₈, using
- net from sequence [i] based on digital (1, 13)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
    - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
digital (134, 154, 1677720)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹⁵⁴, 1677720, F₈, 22, 20) (dual of [(1677720, 22), 36909686, 21]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OOA(8¹⁵⁴, 8388601, F₈, 2, 20) (dual of [(8388601, 2), 16777048, 21]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹⁵⁴, 8388602, F₈, 2, 20) (dual of [(8388602, 2), 16777050, 21]-NRT-code), using
      - trace code [i] based on linear OOA(64⁷⁷, 4194301, F₆₄, 2, 20) (dual of [(4194301, 2), 8388525, 21]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64⁷⁷, 8388602, F₆₄, 20) (dual of [8388602, 8388525, 21]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁷⁷, large, F₆₄, 20) (dual of [large, large−77, 21]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Mode: Constructive and linear.

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