MinT - Best Known (109−5, 109, s)-Nets in Base 16

Best Known (109−5, 109, s)-Nets in Base 16

(109−5, 109, large)-Net over F₁₆ — Constructive and digital

Digital (104, 109, large)-net over F₁₆, using

16⁹ times duplication [i] based on digital (95, 100, large)-net over F₁₆, using
- t-expansion [i] based on digital (89, 100, large)-net over F₁₆, using
  - trace code for nets [i] based on digital (39, 50, 5033159)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256⁵⁰, 5033159, F₂₅₆, 15, 11) (dual of [(5033159, 15), 75497335, 12]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OOA(256⁵⁰, 5033160, F₂₅₆, 5, 11) (dual of [(5033160, 5), 25165750, 12]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁶, 1677720, F₂₅₆, 5, 3) (dual of [(1677720, 5), 8388594, 4]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁶, large, F₂₅₆, 5, 3), using
        appending 2 arbitrary columns [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]
        linear OOA(256¹³, 1677720, F₂₅₆, 5, 5) (dual of [(1677720, 5), 8388587, 6]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹³, 8355839, F₂₅₆, 5, 5) (dual of [(8355839, 5), 41779182, 6]-NRT-code), using
        OOA stacking with additional row [i] based on linear OOA(256¹³, 8355840, F₂₅₆, 2, 5) (dual of [(8355840, 2), 16711667, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 2, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 2, 1) (dual of [(32640, 2), 65279, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 2, 1) with arbitrarily large s, using
        appending 1 arbitrary column [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, 2, 1) (dual of [(32640, 2), 65279, 2]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 2, 1) (dual of [(32640, 2), 65279, 2]-NRT-code) (see above)
        linear OOA(256³, 32640, F₂₅₆, 2, 2) (dual of [(32640, 2), 65277, 3]-NRT-code), using
        discarding factors / shortening the dual code 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, 2, 5) (dual of [(32640, 2), 65273, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256⁷, 65280, F₂₅₆, 5) (dual of [65280, 65273, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
        linear OOA(256³¹, 1677720, F₂₅₆, 5, 11) (dual of [(1677720, 5), 8388569, 12]-NRT-code), using
        OOA 5-folding [i] based on linear OA(256³¹, 8388600, F₂₅₆, 11) (dual of [8388600, 8388569, 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]

(109−5, 109, large)-Net in Base 16 — Upper bound on s

There is no (104, 109, large)-net in base 16, because

3 times m-reduction [i] would yield (104, 106, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]

Best Known (109−5, 109, s)-Nets in Base 16

(109−5, 109, large)-Net over F16 — Constructive and digital

(109−5, 109, large)-Net in Base 16 — Upper bound on s

(109−5, 109, large)-Net over F₁₆ — Constructive and digital