MinT - Best Known (43−8, 43, s)-Nets in Base 64

Best Known (43−8, 43, s)-Nets in Base 64

(43−8, 43, 4194300)-Net over F₆₄ — Constructive and digital

Digital (35, 43, 4194300)-net over F₆₄, using

64¹ times duplication [i] based on digital (34, 42, 4194300)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁴², 4194300, F₆₄, 10, 8) (dual of [(4194300, 10), 41942958, 9]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁴², 8388601, F₆₄, 2, 8) (dual of [(8388601, 2), 16777160, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁴², 8388602, F₆₄, 2, 8) (dual of [(8388602, 2), 16777162, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(64¹³, 4194301, F₆₄, 2, 4) (dual of [(4194301, 2), 8388589, 5]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64¹³, 8388602, F₆₄, 4) (dual of [8388602, 8388589, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹³, large, F₆₄, 4) (dual of [large, large−13, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OOA(64²⁹, 4194301, F₆₄, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64²⁹, 8388602, F₆₄, 8) (dual of [8388602, 8388573, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(64²⁹, large, F₆₄, 8) (dual of [large, large−29, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

(43−8, 43, 4194303)-Net in Base 64 — Constructive

(35, 43, 4194303)-net in base 64, using

64¹ times duplication [i] based on (34, 42, 4194303)-net in base 64, using
- base change [i] based on (28, 36, 4194303)-net in base 128, using
  - net defined by OOA [i] based on OOA(128³⁶, 4194303, S₁₂₈, 12, 8), using
    - OOA stacking with additional row [i] based on OOA(128³⁶, 4194304, S₁₂₈, 4, 8), using
      - discarding parts of the base [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]

(43−8, 43, large)-Net over F₆₄ — Digital

Digital (35, 43, large)-net over F₆₄, using

t-expansion [i] based on digital (34, 43, large)-net over F₆₄, using
- 3 times m-reduction [i] based on digital (34, 46, large)-net over F₆₄, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(64⁴⁶, large, F₆₄, 12) (dual of [large, large−46, 13]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(64⁴⁵, large, F₆₄, 12) (dual of [large, large−45, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

(43−8, 43, large)-Net in Base 64 — Upper bound on s

There is no (35, 43, large)-net in base 64, because

6 times m-reduction [i] would yield (35, 37, large)-net in base 64, but
- mutually orthogonal hypercube bound [i]

Best Known (43−8, 43, s)-Nets in Base 64

(43−8, 43, 4194300)-Net over F64 — Constructive and digital

(43−8, 43, 4194303)-Net in Base 64 — Constructive

(43−8, 43, large)-Net over F64 — Digital

(43−8, 43, large)-Net in Base 64 — Upper bound on s

(43−8, 43, 4194300)-Net over F₆₄ — Constructive and digital

(43−8, 43, large)-Net over F₆₄ — Digital