MinT - Best Known (19, 25, s)-Nets in Base 128

Best Known (19, 25, s)-Nets in Base 128

(19, 25, 2812586)-Net over F₁₂₈ — Constructive and digital

Digital (19, 25, 2812586)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 4, 16385)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128⁴, 16385, F₁₂₈, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁴, 16385, F₁₂₈, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁴, 16385, F₁₂₈, 3) (dual of [16385, 16381, 4]-code or 16385-cap in PG(3,128)), using
        ovoid in PG(3,Â 128) [i]
2. digital (15, 21, 2796201)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128²¹, 2796201, F₁₂₈, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
    - OA 3-folding and stacking [i] 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]

(19, 25, 5592576)-Net in Base 128 — Constructive

(19, 25, 5592576)-net in base 128, using

128¹ times duplication [i] based on (18, 24, 5592576)-net in base 128, using
- base change [i] based on digital (15, 21, 5592576)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256²¹, 5592576, F₂₅₆, 6, 6) (dual of [(5592576, 6), 33555435, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(256²¹, 5592576, F₂₅₆, 5, 6) (dual of [(5592576, 5), 27962859, 7]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 5, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256⁰, 21846, F₂₅₆, 5, 0) (dual of [(21846, 5), 109230, 1]-NRT-code) (see above)
        linear OOA(256¹, 21846, F₂₅₆, 5, 1) (dual of [(21846, 5), 109229, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 5, 1) with arbitrarily large s, using
        appending 4 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, 21846, F₂₅₆, 5, 1) (dual of [(21846, 5), 109229, 2]-NRT-code) (see above)
        linear OOA(256¹, 21846, F₂₅₆, 5, 1) (dual of [(21846, 5), 109229, 2]-NRT-code) (see above)
        linear OOA(256³, 21846, F₂₅₆, 5, 2) (dual of [(21846, 5), 109227, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256³, 65793, F₂₅₆, 5, 2) (dual of [(65793, 5), 328962, 3]-NRT-code), using
        appending 3 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(256⁴, 21846, F₂₅₆, 5, 3) (dual of [(21846, 5), 109226, 4]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁴, 65537, F₂₅₆, 5, 3) (dual of [(65537, 5), 327681, 4]-NRT-code), using
        appending 2 arbitrary columns [i] based on linear OOA(256⁴, 65537, F₂₅₆, 3, 3) (dual of [(65537, 3), 196607, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(256⁴, 65537, F₂₅₆, 2, 3) (dual of [(65537, 2), 131070, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [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(256¹¹, 21846, F₂₅₆, 5, 6) (dual of [(21846, 5), 109219, 7]-NRT-code), using
        OA 3-folding and stacking [i] based on linear OA(256¹¹, 65538, F₂₅₆, 6) (dual of [65538, 65527, 7]-code), using
        constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(256⁹, 65536, F₂₅₆, 5) (dual of [65536, 65527, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

(19, 25, large)-Net over F₁₂₈ — Digital

Digital (19, 25, large)-net over F₁₂₈, using

t-expansion [i] based on digital (18, 25, large)-net over F₁₂₈, using
- Gilbertâ€“VarÅ¡amov bound [i]

(19, 25, large)-Net in Base 128 — Upper bound on s

There is no (19, 25, large)-net in base 128, because

4 times m-reduction [i] would yield (19, 21, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (19, 25, s)-Nets in Base 128

(19, 25, 2812586)-Net over F128 — Constructive and digital

(19, 25, 5592576)-Net in Base 128 — Constructive

(19, 25, large)-Net over F128 — Digital

(19, 25, large)-Net in Base 128 — Upper bound on s

(19, 25, 2812586)-Net over F₁₂₈ — Constructive and digital

(19, 25, large)-Net over F₁₂₈ — Digital