MinT - Information on Result #1191328

Information on Result #1191328

Digital (73, 83, 2796233)-net over F₈, using net defined by OOA based on linear OOA(8⁸³, 2796233, F₈, 15, 10) (dual of [(2796233, 15), 41943412, 11]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(8⁸³, 5592467, F₈, 3, 10) (dual of [(5592467, 3), 16777318, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁹, 65, F₈, 3, 5) (dual of [(65, 3), 186, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 9, 65)-net over F₈, using
      - base reduction for projective spaces (embedding PG(4,64) in PG(8,8)) for nets [i] based on digital (0, 5, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
  2. linear OOA(8⁷⁴, 5592402, F₈, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
    - trace code [i] based on linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
      - OOA 3-folding [i] 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.