MinT - Best Known (44−10, 44, s)-Nets in Base 128

Best Known (44−10, 44, s)-Nets in Base 128

(44−10, 44, 1685848)-Net over F₁₂₈ — Constructive and digital

Digital (34, 44, 1685848)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (2, 7, 8128)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128⁷, 8128, F₁₂₈, 5, 5) (dual of [(8128, 5), 40633, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁷, 8128, F₁₂₈, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
2. digital (27, 37, 1677720)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128³⁷, 1677720, F₁₂₈, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
    - OA 5-folding and stacking [i] based on linear OA(128³⁷, 8388600, F₁₂₈, 10) (dual of [8388600, 8388563, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(128³⁷, large, F₁₂₈, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

(44−10, 44, 1743512)-Net in Base 128 — Constructive

(34, 44, 1743512)-net in base 128, using

(u,Â u+v)-construction [i] based on
1. (7, 12, 65792)-net in base 128, using
  - net defined by OOA [i] based on OOA(128¹², 65792, S₁₂₈, 5, 5), using
    - appending kth column [i] based on OOA(128¹², 65792, S₁₂₈, 4, 5), using
      - discarding parts of the base [i] based on linear OOA(256¹⁰, 65792, F₂₅₆, 4, 5) (dual of [(65792, 4), 263158, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 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, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 4, 0) (dual of [(257, 4), 1028, 1]-NRT-code) (see above)
        linear OOA(256¹, 257, F₂₅₆, 4, 1) (dual of [(257, 4), 1027, 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, 257, F₂₅₆, 4, 1) (dual of [(257, 4), 1027, 2]-NRT-code) (see above)
        linear OOA(256¹, 257, F₂₅₆, 4, 1) (dual of [(257, 4), 1027, 2]-NRT-code) (see above)
        linear OOA(256², 257, F₂₅₆, 4, 2) (dual of [(257, 4), 1026, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;1026,256) [i]
        linear OOA(256⁵, 257, F₂₅₆, 4, 5) (dual of [(257, 4), 1023, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;1023,256) [i]
2. (22, 32, 1677720)-net in base 128, using
  - base change [i] based on digital (18, 28, 1677720)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256²⁸, 1677720, F₂₅₆, 10, 10) (dual of [(1677720, 10), 16777172, 11]-NRT-code), using
      - OA 5-folding and stacking [i] based on linear OA(256²⁸, 8388600, F₂₅₆, 10) (dual of [8388600, 8388572, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(256²⁸, large, F₂₅₆, 10) (dual of [large, large−28, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

(44−10, 44, large)-Net over F₁₂₈ — Digital

Digital (34, 44, large)-net over F₁₂₈, using

t-expansion [i] based on digital (32, 44, large)-net over F₁₂₈, using
- Gilbertâ€“VarÅ¡amov bound [i]

(44−10, 44, large)-Net in Base 128 — Upper bound on s

There is no (34, 44, large)-net in base 128, because

8 times m-reduction [i] would yield (34, 36, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (44−10, 44, s)-Nets in Base 128

(44−10, 44, 1685848)-Net over F128 — Constructive and digital

(44−10, 44, 1743512)-Net in Base 128 — Constructive

(44−10, 44, large)-Net over F128 — Digital

(44−10, 44, large)-Net in Base 128 — Upper bound on s

(44−10, 44, 1685848)-Net over F₁₂₈ — Constructive and digital

(44−10, 44, large)-Net over F₁₂₈ — Digital