MinT - Best Known (57, 57+6, s)-Nets in Base 16

Best Known (57, 57+6, s)-Nets in Base 16

(57, 57+6, large)-Net over F₁₆ — Constructive and digital

Digital (57, 63, large)-net over F₁₆, using

16¹ times duplication [i] based on digital (56, 62, large)-net over F₁₆, using
- t-expansion [i] based on digital (54, 62, large)-net over F₁₆, using
  - trace code for nets [i] based on digital (23, 31, 4194303)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256³¹, 4194303, F₂₅₆, 12, 8) (dual of [(4194303, 12), 50331605, 9]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(256³¹, 4194304, F₂₅₆, 4, 8) (dual of [(4194304, 4), 16777185, 9]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 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, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16384, F₂₅₆, 4, 0) (dual of [(16384, 4), 65536, 1]-NRT-code) (see above)
        linear OOA(256¹, 16384, F₂₅₆, 4, 1) (dual of [(16384, 4), 65535, 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, 16384, F₂₅₆, 4, 1) (dual of [(16384, 4), 65535, 2]-NRT-code) (see above)
        linear OOA(256¹, 16384, F₂₅₆, 4, 1) (dual of [(16384, 4), 65535, 2]-NRT-code) (see above)
        linear OOA(256¹, 16384, F₂₅₆, 4, 1) (dual of [(16384, 4), 65535, 2]-NRT-code) (see above)
        linear OOA(256³, 16384, F₂₅₆, 4, 2) (dual of [(16384, 4), 65533, 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(256³, 16384, F₂₅₆, 4, 2) (dual of [(16384, 4), 65533, 3]-NRT-code) (see above)
        linear OOA(256⁶, 16384, F₂₅₆, 4, 4) (dual of [(16384, 4), 65530, 5]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁶, 32640, F₂₅₆, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(256⁶, 65280, F₂₅₆, 4) (dual of [65280, 65274, 5]-code), using
        1 times truncation [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
        linear OOA(256¹⁵, 16384, F₂₅₆, 4, 8) (dual of [(16384, 4), 65521, 9]-NRT-code), using
        OOA 4-folding [i] based on linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using
        an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

(57, 57+6, large)-Net in Base 16 — Upper bound on s

There is no (57, 63, large)-net in base 16, because

4 times m-reduction [i] would yield (57, 59, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]

Best Known (57, 57+6, s)-Nets in Base 16

(57, 57+6, large)-Net over F16 — Constructive and digital

(57, 57+6, large)-Net in Base 16 — Upper bound on s

(57, 57+6, large)-Net over F₁₆ — Constructive and digital