MinT - Best Known (21−4, 21, s)-Nets in Base 128

Best Known (21−4, 21, s)-Nets in Base 128

(21−4, 21, large)-Net over F₁₂₈ — Constructive and digital

Digital (17, 21, large)-net over F₁₂₈, using

128¹ times duplication [i] based on digital (16, 20, large)-net over F₁₂₈, using
- t-expansion [i] based on digital (15, 20, large)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128²⁰, large, F₁₂₈, 5, 5), using
    - appending kth column [i] based on linear OOA(128²⁰, large, F₁₂₈, 4, 5), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 4, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128⁰, 1048577, F₁₂₈, 4, 0) (dual of [(1048577, 4), 4194308, 1]-NRT-code) (see above)
        linear OOA(128¹, 1048577, F₁₂₈, 4, 1) (dual of [(1048577, 4), 4194307, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 4, 1) with arbitrarily large s, using
        appending 3 arbitrary columns [i] based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
        parity-check code [i]
        linear OOA(128¹, 1048577, F₁₂₈, 4, 1) (dual of [(1048577, 4), 4194307, 2]-NRT-code) (see above)
        linear OOA(128¹, 1048577, F₁₂₈, 4, 1) (dual of [(1048577, 4), 4194307, 2]-NRT-code) (see above)
        linear OOA(128⁴, 1048577, F₁₂₈, 4, 2) (dual of [(1048577, 4), 4194304, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(128⁴, 2113665, F₁₂₈, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(128⁴, 2113665, F₁₂₈, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
        appending kth column [i] based on linear OA(128⁴, 2113665, F₁₂₈, 2) (dual of [2113665, 2113661, 3]-code), using
        Hamming code H(4,128) [i]
        linear OOA(128¹³, 1048577, F₁₂₈, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(128¹³, 2097155, F₁₂₈, 5) (dual of [2097155, 2097142, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(128¹³, 2097152, F₁₂₈, 5) (dual of [2097152, 2097139, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

(21−4, 21, large)-Net in Base 128 — Upper bound on s

There is no (17, 21, large)-net in base 128, because

2 times m-reduction [i] would yield (17, 19, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (21−4, 21, s)-Nets in Base 128

(21−4, 21, large)-Net over F128 — Constructive and digital

(21−4, 21, large)-Net in Base 128 — Upper bound on s

(21−4, 21, large)-Net over F₁₂₈ — Constructive and digital