MinT - Information on Result #1215171

Information on Result #1215171

Digital (101, 112, 3355468)-net over F₈, using (u,Â u+v)-construction based on

digital (28, 33, 4194301)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8³³, 4194301, F₈, 5, 5) (dual of [(4194301, 5), 20971472, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(8³³, large, F₈, 5) (dual of [large, large−33, 6]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
digital (68, 79, 1677734)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 6, 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]
  2. digital (62, 73, 1677720)-net over F₈, using
    - net defined by OOA [i] based on linear OOA(8⁷³, 1677720, F₈, 11, 11) (dual of [(1677720, 11), 18454847, 12]-NRT-code), using
      - OOA 5-folding and stacking with additional row [i] based on linear OA(8⁷³, 8388601, F₈, 11) (dual of [8388601, 8388528, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁷³, large, F₈, 11) (dual of [large, large−73, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.