MinT - Best Known (39, 39+11, s)-Nets in Base 256

Best Known (39, 39+11, s)-Nets in Base 256

(39, 39+11, 5033160)-Net over F₂₅₆ — Constructive and digital

Digital (39, 50, 5033160)-net over F₂₅₆, using

generalized (u,Â u+v)-construction [i] based on
1. digital (3, 6, 1677720)-net over F₂₅₆, using
  - s-reduction based on digital (3, 6, large)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256⁶, large, F₂₅₆, 3, 3), using
      - appending kth column [i] based on linear OOA(256⁶, large, F₂₅₆, 2, 3), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(256⁶, large, F₂₅₆, 3) (dual of [large, large−6, 4]-code), using
        product of projective cap with (hyper)oval [i] based on linear OA(256⁴, 65537, F₂₅₆, 3) (dual of [65537, 65533, 4]-code or 65537-cap in PG(3,256)), using
        ovoid in PG(3,Â 256) [i]
2. digital (8, 13, 1677720)-net over F₂₅₆, using
  - s-reduction based on digital (8, 13, 8355840)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256¹³, 8355840, F₂₅₆, 5, 5) (dual of [(8355840, 5), 41779187, 6]-NRT-code), using
      - appending kth column [i] based on linear OOA(256¹³, 8355840, F₂₅₆, 4, 5) (dual of [(8355840, 4), 33423347, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 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, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 4, 1) (dual of [(32640, 4), 130559, 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, 32640, F₂₅₆, 4, 1) (dual of [(32640, 4), 130559, 2]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 4, 1) (dual of [(32640, 4), 130559, 2]-NRT-code) (see above)
        linear OOA(256³, 32640, F₂₅₆, 4, 2) (dual of [(32640, 4), 130557, 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(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]
3. digital (20, 31, 1677720)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256³¹, 1677720, F₂₅₆, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(256³¹, 8388601, F₂₅₆, 11) (dual of [8388601, 8388570, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(256³¹, large, F₂₅₆, 11) (dual of [large, large−31, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

(39, 39+11, large)-Net over F₂₅₆ — Digital

Digital (39, 50, large)-net over F₂₅₆, using

t-expansion [i] based on digital (38, 50, large)-net over F₂₅₆, using
- 5 times m-reduction [i] based on digital (38, 55, large)-net over F₂₅₆, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(256⁵⁵, large, F₂₅₆, 17) (dual of [large, large−55, 18]-code), using
    - strength reduction [i] based on linear OA(256⁵⁵, large, F₂₅₆, 19) (dual of [large, large−55, 20]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

(39, 39+11, large)-Net in Base 256 — Upper bound on s

There is no (39, 50, large)-net in base 256, because

9 times m-reduction [i] would yield (39, 41, large)-net in base 256, but
- mutually orthogonal hypercube bound [i]

Best Known (39, 39+11, s)-Nets in Base 256

(39, 39+11, 5033160)-Net over F256 — Constructive and digital

(39, 39+11, large)-Net over F256 — Digital

(39, 39+11, large)-Net in Base 256 — Upper bound on s

(39, 39+11, 5033160)-Net over F₂₅₆ — Constructive and digital

(39, 39+11, large)-Net over F₂₅₆ — Digital