MinT - Best Known (49, 60, s)-Nets in Base 128

Best Known (49, 60, s)-Nets in Base 128

(49, 60, 3774874)-Net over F₁₂₈ — Constructive and digital

Digital (49, 60, 3774874)-net over F₁₂₈, using

generalized (u,Â u+v)-construction [i] based on
1. digital (3, 6, 1048577)-net over F₁₂₈, using
  - s-reduction based on digital (3, 6, 2130050)-net over F₁₂₈, using
    - net defined by OOA [i] based on linear OOA(128⁶, 2130050, F₁₂₈, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(128⁶, 2130050, F₁₂₈, 2, 3) (dual of [(2130050, 2), 4260094, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁶, 2130050, F₁₂₈, 3) (dual of [2130050, 2130044, 4]-code or 2130050-cap in PG(5,128)), using
        large caps in PG(5,Â b) [i]
2. digital (8, 13, 1048577)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128¹³, 1048577, F₁₂₈, 5, 5) (dual of [(1048577, 5), 5242872, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(128¹³, 1048577, F₁₂₈, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(128¹³, 2097155, F₁₂₈, 5) (dual of [2097155, 2097142, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(128¹³, 2097152, F₁₂₈, 5) (dual of [2097152, 2097139, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        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(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]
3. digital (30, 41, 1677720)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128⁴¹, 1677720, F₁₂₈, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(128⁴¹, 8388601, F₁₂₈, 11) (dual of [8388601, 8388560, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

(49, 60, 4194301)-Net in Base 128 — Constructive

(49, 60, 4194301)-net in base 128, using

128² times duplication [i] based on (47, 58, 4194301)-net in base 128, using
- net defined by OOA [i] based on OOA(128⁵⁸, 4194301, S₁₂₈, 15, 11), using
  - OOA 2-folding and stacking with additional row [i] based on OOA(128⁵⁸, large, S₁₂₈, 3, 11), using
    - discarding parts of the base [i] based on linear OOA(256⁵⁰, large, F₂₅₆, 3, 11), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁶, 2796201, F₂₅₆, 3, 3) (dual of [(2796201, 3), 8388597, 4]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁶, 8388602, F₂₅₆, 3, 3) (dual of [(8388602, 3), 25165800, 4]-NRT-code), using
        OOA stacking with additional row [i] based on linear OA(256⁶, large, F₂₅₆, 3) (dual of [large, large−6, 4]-code), using
        product of projective cap with (hyper)oval [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(256¹³, 2796201, F₂₅₆, 3, 5) (dual of [(2796201, 3), 8388590, 6]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹³, 8355839, F₂₅₆, 3, 5) (dual of [(8355839, 3), 25067504, 6]-NRT-code), using
        OOA stacking with additional row [i] based on linear OOA(256¹³, 8355840, F₂₅₆, 2, 5) (dual of [(8355840, 2), 16711667, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 2, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 2, 0) (dual of [(32640, 2), 65280, 1]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 2, 1) (dual of [(32640, 2), 65279, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 2, 1) with arbitrarily large s, using
        appending 1 arbitrary column [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, 32640, F₂₅₆, 2, 1) (dual of [(32640, 2), 65279, 2]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 2, 1) (dual of [(32640, 2), 65279, 2]-NRT-code) (see above)
        linear OOA(256³, 32640, F₂₅₆, 2, 2) (dual of [(32640, 2), 65277, 3]-NRT-code), using
        discarding factors / shortening the dual code 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(256⁷, 32640, F₂₅₆, 2, 5) (dual of [(32640, 2), 65273, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256⁷, 65280, F₂₅₆, 5) (dual of [65280, 65273, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
        linear OOA(256³¹, 2796201, F₂₅₆, 3, 11) (dual of [(2796201, 3), 8388572, 12]-NRT-code), using
        OOA 3-folding [i] based on linear OA(256³¹, large, F₂₅₆, 11) (dual of [large, large−31, 12]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

(49, 60, large)-Net over F₁₂₈ — Digital

Digital (49, 60, large)-net over F₁₂₈, using

t-expansion [i] based on digital (48, 60, large)-net over F₁₂₈, using
- 6 times m-reduction [i] based on digital (48, 66, large)-net over F₁₂₈, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(49, 60, large)-Net in Base 128 — Upper bound on s

There is no (49, 60, large)-net in base 128, because

9 times m-reduction [i] would yield (49, 51, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (49, 60, s)-Nets in Base 128

(49, 60, 3774874)-Net over F128 — Constructive and digital

(49, 60, 4194301)-Net in Base 128 — Constructive

(49, 60, large)-Net over F128 — Digital

(49, 60, large)-Net in Base 128 — Upper bound on s

(49, 60, 3774874)-Net over F₁₂₈ — Constructive and digital

(49, 60, large)-Net over F₁₂₈ — Digital