MinT - Best Known (31, 31+8, s)-Nets in Base 128

Best Known (31, 31+8, s)-Nets in Base 128

(31, 31+8, 3145727)-Net over F₁₂₈ — Constructive and digital

Digital (31, 39, 3145727)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (6, 10, 1048577)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128¹⁰, 1048577, F₁₂₈, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(128¹⁰, 2097154, F₁₂₈, 4) (dual of [2097154, 2097144, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(128¹⁰, 2097155, F₁₂₈, 4) (dual of [2097155, 2097145, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(128⁷, 2097152, F₁₂₈, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
2. digital (21, 29, 2097150)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128²⁹, 2097150, F₁₂₈, 8, 8) (dual of [(2097150, 8), 16777171, 9]-NRT-code), using
    - OA 4-folding and stacking [i] based on linear OA(128²⁹, 8388600, F₁₂₈, 8) (dual of [8388600, 8388571, 9]-code), using
      - discarding factors / shortening the dual code based on linear OA(128²⁹, large, F₁₂₈, 8) (dual of [large, large−29, 9]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

(31, 31+8, 4194815)-Net in Base 128 — Constructive

(31, 39, 4194815)-net in base 128, using

128¹ times duplication [i] based on (30, 38, 4194815)-net in base 128, using
- net defined by OOA [i] based on OOA(128³⁸, 4194815, S₁₂₈, 12, 8), using
  - OOA stacking with additional row [i] based on OOA(128³⁸, 4194816, S₁₂₈, 4, 8), using
    - discarding parts of the base [i] based on linear OOA(256³³, 4194816, F₂₅₆, 4, 8) (dual of [(4194816, 4), 16779231, 9]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 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, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256⁰, 16386, F₂₅₆, 4, 0) (dual of [(16386, 4), 65544, 1]-NRT-code) (see above)
        linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 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, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code) (see above)
        linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code) (see above)
        linear OOA(256¹, 16386, F₂₅₆, 4, 1) (dual of [(16386, 4), 65543, 2]-NRT-code) (see above)
        linear OOA(256³, 16386, F₂₅₆, 4, 2) (dual of [(16386, 4), 65541, 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, 16386, F₂₅₆, 4, 2) (dual of [(16386, 4), 65541, 3]-NRT-code) (see above)
        linear OOA(256⁶, 16386, F₂₅₆, 4, 4) (dual of [(16386, 4), 65538, 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(256¹⁷, 16386, F₂₅₆, 4, 8) (dual of [(16386, 4), 65527, 9]-NRT-code), using
        OOA 4-folding [i] based on linear OA(256¹⁷, 65544, F₂₅₆, 8) (dual of [65544, 65527, 9]-code), using
        constructionÂ X applied to C_e(7) âŠ‚ C_e(4) [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]
        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(256², 8, F₂₅₆, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
        discarding factors / shortening the dual code based on linear OA(256², 256, F₂₅₆, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
        Reedâ€“Solomon code RS(254,256) [i]

(31, 31+8, large)-Net over F₁₂₈ — Digital

Digital (31, 39, large)-net over F₁₂₈, using

t-expansion [i] based on digital (29, 39, large)-net over F₁₂₈, using
- 1 times m-reduction [i] based on digital (29, 40, large)-net over F₁₂₈, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(31, 31+8, large)-Net in Base 128 — Upper bound on s

There is no (31, 39, large)-net in base 128, because

6 times m-reduction [i] would yield (31, 33, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (31, 31+8, s)-Nets in Base 128

(31, 31+8, 3145727)-Net over F128 — Constructive and digital

(31, 31+8, 4194815)-Net in Base 128 — Constructive

(31, 31+8, large)-Net over F128 — Digital

(31, 31+8, large)-Net in Base 128 — Upper bound on s

(31, 31+8, 3145727)-Net over F₁₂₈ — Constructive and digital

(31, 31+8, large)-Net over F₁₂₈ — Digital