MinT - Best Known (57, 57+13, s)-Nets in Base 128

Best Known (57, 57+13, s)-Nets in Base 128

(57, 57+13, 2796200)-Net over F₁₂₈ — Constructive and digital

Digital (57, 70, 2796200)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128⁷⁰, 2796200, F₁₂₈, 14, 13) (dual of [(2796200, 14), 39146730, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(128⁷⁰, 8388601, F₁₂₈, 2, 13) (dual of [(8388601, 2), 16777132, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(128⁷⁰, 8388602, F₁₂₈, 2, 13) (dual of [(8388602, 2), 16777134, 14]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(128²¹, 4194301, F₁₂₈, 2, 6) (dual of [(4194301, 2), 8388581, 7]-NRT-code), using
        OOA 2-folding [i] based on linear OA(128²¹, 8388602, F₁₂₈, 6) (dual of [8388602, 8388581, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(128²¹, large, F₁₂₈, 6) (dual of [large, large−21, 7]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      2. linear OOA(128⁴⁹, 4194301, F₁₂₈, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
        OOA 2-folding [i] based on linear OA(128⁴⁹, 8388602, F₁₂₈, 13) (dual of [8388602, 8388553, 14]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁴⁹, large, F₁₂₈, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

(57, 57+13, 2829096)-Net in Base 128 — Constructive

(57, 70, 2829096)-net in base 128, using

net defined by OOA [i] based on OOA(128⁷⁰, 2829096, S₁₂₈, 15, 13), using
- OOA 2-folding and stacking with additional row [i] based on OOA(128⁷⁰, 5658193, S₁₂₈, 3, 13), using
  - discarding factors based on OOA(128⁷⁰, 5658194, S₁₂₈, 3, 13), using
    - discarding parts of the base [i] based on linear OOA(256⁶¹, 5658194, F₂₅₆, 3, 13) (dual of [(5658194, 3), 16974521, 14]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁸, 65792, F₂₅₆, 3, 4) (dual of [(65792, 3), 197368, 5]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 3, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256¹, 257, F₂₅₆, 3, 1) (dual of [(257, 3), 770, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 3, 1) with arbitrarily large s, using
        appending 2 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, 257, F₂₅₆, 3, 1) (dual of [(257, 3), 770, 2]-NRT-code) (see above)
        linear OOA(256², 257, F₂₅₆, 3, 2) (dual of [(257, 3), 769, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;769,256) [i]
        linear OOA(256⁴, 257, F₂₅₆, 3, 4) (dual of [(257, 3), 767, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;767,256) [i]
        linear OOA(256¹⁶, 2796201, F₂₅₆, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OOA(256³⁷, 2796201, F₂₅₆, 3, 13) (dual of [(2796201, 3), 8388566, 14]-NRT-code), using
        OOA 3-folding [i] based on linear OA(256³⁷, large, F₂₅₆, 13) (dual of [large, large−37, 14]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

(57, 57+13, large)-Net over F₁₂₈ — Digital

Digital (57, 70, large)-net over F₁₂₈, using

t-expansion [i] based on digital (56, 70, large)-net over F₁₂₈, using
- 7 times m-reduction [i] based on digital (56, 77, large)-net over F₁₂₈, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+13, large)-Net in Base 128 — Upper bound on s

There is no (57, 70, large)-net in base 128, because

11 times m-reduction [i] would yield (57, 59, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (57, 57+13, s)-Nets in Base 128

(57, 57+13, 2796200)-Net over F128 — Constructive and digital

(57, 57+13, 2829096)-Net in Base 128 — Constructive

(57, 57+13, large)-Net over F128 — Digital

(57, 57+13, large)-Net in Base 128 — Upper bound on s

(57, 57+13, 2796200)-Net over F₁₂₈ — Constructive and digital

(57, 57+13, large)-Net over F₁₂₈ — Digital