MinT - Best Known (68−12, 68, s)-Nets in Base 128

Best Known (68−12, 68, s)-Nets in Base 128

(68−12, 68, 2796200)-Net over F₁₂₈ — Constructive and digital

Digital (56, 68, 2796200)-net over F₁₂₈, using

128² times duplication [i] based on digital (54, 66, 2796200)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁶⁶, 2796200, F₁₂₈, 14, 12) (dual of [(2796200, 14), 39146734, 13]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OOA(128⁶⁶, 8388601, F₁₂₈, 2, 12) (dual of [(8388601, 2), 16777136, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁶⁶, 8388602, F₁₂₈, 2, 12) (dual of [(8388602, 2), 16777138, 13]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(128²¹, 4194301, F₁₂₈, 2, 6) (dual of [(4194301, 2), 8388581, 7]-NRT-code), using
        OOA 2-folding [i] based on linear OA(128²¹, 8388602, F₁₂₈, 6) (dual of [8388602, 8388581, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(128²¹, large, F₁₂₈, 6) (dual of [large, large−21, 7]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OOA(128⁴⁵, 4194301, F₁₂₈, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
        OOA 2-folding [i] based on linear OA(128⁴⁵, 8388602, F₁₂₈, 12) (dual of [8388602, 8388557, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁴⁵, large, F₁₂₈, 12) (dual of [large, large−45, 13]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

(68−12, 68, 2829097)-Net in Base 128 — Constructive

(56, 68, 2829097)-net in base 128, using

net defined by OOA [i] based on OOA(128⁶⁸, 2829097, S₁₂₈, 15, 12), using
- OOA 2-folding and stacking with additional row [i] based on OOA(128⁶⁸, 5658195, S₁₂₈, 3, 12), using
  - discarding parts of the base [i] based on linear OOA(256⁵⁹, 5658195, F₂₅₆, 3, 12) (dual of [(5658195, 3), 16974526, 13]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(256⁹, 65793, F₂₅₆, 3, 4) (dual of [(65793, 3), 197370, 5]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 3, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 3, 0) (dual of [(257, 3), 771, 1]-NRT-code) (see above)
        linear OOA(256¹, 257, F₂₅₆, 3, 1) (dual of [(257, 3), 770, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 3, 1) with arbitrarily large s, using
        appending 2 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, 257, F₂₅₆, 3, 1) (dual of [(257, 3), 770, 2]-NRT-code) (see above)
        linear OOA(256², 257, F₂₅₆, 3, 2) (dual of [(257, 3), 769, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;769,256) [i]
        linear OOA(256⁵, 258, F₂₅₆, 3, 4) (dual of [(258, 3), 769, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (1, 5, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
      2. linear OOA(256¹⁶, 2796201, F₂₅₆, 3, 6) (dual of [(2796201, 3), 8388587, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(256¹⁶, large, F₂₅₆, 6) (dual of [large, large−16, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OOA(256³⁴, 2796201, F₂₅₆, 3, 12) (dual of [(2796201, 3), 8388569, 13]-NRT-code), using
        OOA 3-folding [i] based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

(68−12, 68, large)-Net over F₁₂₈ — Digital

Digital (56, 68, large)-net over F₁₂₈, using

9 times m-reduction [i] based on digital (56, 77, large)-net over F₁₂₈, using
- Gilbertâ€“VarÅ¡amov bound [i]

(68−12, 68, large)-Net in Base 128 — Upper bound on s

There is no (56, 68, large)-net in base 128, because

10 times m-reduction [i] would yield (56, 58, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (68−12, 68, s)-Nets in Base 128

(68−12, 68, 2796200)-Net over F128 — Constructive and digital

(68−12, 68, 2829097)-Net in Base 128 — Constructive

(68−12, 68, large)-Net over F128 — Digital

(68−12, 68, large)-Net in Base 128 — Upper bound on s

(68−12, 68, 2796200)-Net over F₁₂₈ — Constructive and digital

(68−12, 68, large)-Net over F₁₂₈ — Digital