MinT - Best Known (19−5, 19, s)-Nets in Base 128

Best Known (19−5, 19, s)-Nets in Base 128

(19−5, 19, 4194430)-Net over F₁₂₈ — Constructive and digital

Digital (14, 19, 4194430)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128¹⁹, 4194430, F₁₂₈, 5, 5) (dual of [(4194430, 5), 20972131, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(128¹⁹, 4194430, F₁₂₈, 4, 5) (dual of [(4194430, 4), 16777701, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. 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]
    2. 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]

(19−5, 19, large)-Net in Base 128 — Constructive

(14, 19, large)-net in base 128, using

128¹ times duplication [i] based on (13, 18, large)-net in base 128, using
- net defined by OOA [i] based on OOA(128¹⁸, large, S₁₂₈, 5, 5), using
  - appending kth column [i] based on OOA(128¹⁸, large, S₁₂₈, 4, 5), using
    - discarding parts of the base [i] based on linear OOA(256¹⁵, large, F₂₅₆, 4, 5), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 4, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32897, F₂₅₆, 4, 0) (dual of [(32897, 4), 131588, 1]-NRT-code) (see above)
        linear OOA(256¹, 32897, F₂₅₆, 4, 1) (dual of [(32897, 4), 131587, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 4, 1) with arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
        parity-check code [i]
        linear OOA(256¹, 32897, F₂₅₆, 4, 1) (dual of [(32897, 4), 131587, 2]-NRT-code) (see above)
        linear OOA(256¹, 32897, F₂₅₆, 4, 1) (dual of [(32897, 4), 131587, 2]-NRT-code) (see above)
        linear OOA(256³, 32897, F₂₅₆, 4, 2) (dual of [(32897, 4), 131585, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256³, 65793, F₂₅₆, 4, 2) (dual of [(65793, 4), 263169, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(256³, 65793, F₂₅₆, 2, 2) (dual of [(65793, 2), 131583, 3]-NRT-code), using
        appending kth column [i] based on linear OA(256³, 65793, F₂₅₆, 2) (dual of [65793, 65790, 3]-code), using
        Hamming code H(3,256) [i]
        linear OOA(256⁹, 32897, F₂₅₆, 4, 5) (dual of [(32897, 4), 131579, 6]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(256², 257, F₂₅₆, 4, 2) (dual of [(257, 4), 1026, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;1026,256) [i]
        linear OOA(256⁷, 32640, F₂₅₆, 4, 5) (dual of [(32640, 4), 130553, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]

(19−5, 19, large)-Net over F₁₂₈ — Digital

Digital (14, 19, large)-net over F₁₂₈, using

128² times duplication [i] based on digital (12, 17, large)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128¹⁷, large, F₁₂₈, 5, 5), using
  - appending kth column [i] based on linear OOA(128¹⁷, large, F₁₂₈, 4, 5), using
    - Gilbertâ€“VarÅ¡amov bound [i]

(19−5, 19, large)-Net in Base 128 — Upper bound on s

There is no (14, 19, large)-net in base 128, because

3 times m-reduction [i] would yield (14, 16, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (19−5, 19, s)-Nets in Base 128

(19−5, 19, 4194430)-Net over F128 — Constructive and digital

(19−5, 19, large)-Net in Base 128 — Constructive

(19−5, 19, large)-Net over F128 — Digital

(19−5, 19, large)-Net in Base 128 — Upper bound on s

(19−5, 19, 4194430)-Net over F₁₂₈ — Constructive and digital

(19−5, 19, large)-Net over F₁₂₈ — Digital