MinT - Information on Result #1228135

Information on Result #1228135

Digital (63, 74, 6710880)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (12, 17, 4194301)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128¹⁷, 4194301, F₁₂₈, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(128¹⁷, 4194301, F₁₂₈, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(128¹⁷, large, F₁₂₈, 5) (dual of [large, large−17, 6]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
digital (46, 57, 3355440)-net over F₁₂₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 16, 2113536)-net over F₁₂₈, using
    - net defined by OOA [i] based on linear OOA(128¹⁶, 2113536, F₁₂₈, 5, 5) (dual of [(2113536, 5), 10567664, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(128¹⁶, 2113536, F₁₂₈, 4, 5) (dual of [(2113536, 4), 8454128, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 4, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128⁰, 16512, F₁₂₈, 4, 0) (dual of [(16512, 4), 66048, 1]-NRT-code) (see above)
        linear OOA(128¹, 16512, F₁₂₈, 4, 1) (dual of [(16512, 4), 66047, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 4, 1) for arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
        linear OOA(128¹, 16512, F₁₂₈, 4, 1) (dual of [(16512, 4), 66047, 2]-NRT-code) (see above)
        linear OOA(128¹, 16512, F₁₂₈, 4, 1) (dual of [(16512, 4), 66047, 2]-NRT-code) (see above)
        linear OOA(128³, 16512, F₁₂₈, 4, 2) (dual of [(16512, 4), 66045, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128³, 16513, F₁₂₈, 4, 2) (dual of [(16513, 4), 66049, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(128³, 16513, F₁₂₈, 2, 2) (dual of [(16513, 2), 33023, 3]-NRT-code), using
        appending kth column [i] based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
        Hamming code H(3,128) [i]
        linear OOA(128¹⁰, 16512, F₁₂₈, 4, 5) (dual of [(16512, 4), 66038, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 4, 0) for arbitrarily large s (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128⁰, 129, F₁₂₈, 4, 0) (dual of [(129, 4), 516, 1]-NRT-code) (see above)
        linear OOA(128¹, 129, F₁₂₈, 4, 1) (dual of [(129, 4), 515, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 4, 1) for arbitrarily large s (see above)
        linear OOA(128¹, 129, F₁₂₈, 4, 1) (dual of [(129, 4), 515, 2]-NRT-code) (see above)
        linear OOA(128¹, 129, F₁₂₈, 4, 1) (dual of [(129, 4), 515, 2]-NRT-code) (see above)
        linear OOA(128², 129, F₁₂₈, 4, 2) (dual of [(129, 4), 514, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;514,128) [i]
        linear OOA(128⁵, 129, F₁₂₈, 4, 5) (dual of [(129, 4), 511, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;511,128) [i]
  2. digital (30, 41, 1677720)-net over F₁₂₈, using
    - net defined by OOA [i] based on linear OOA(128⁴¹, 1677720, F₁₂₈, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
      - OOA 5-folding and stacking with additional row [i] based on linear OA(128⁴¹, 8388601, F₁₂₈, 11) (dual of [8388601, 8388560, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.