MinT - Best Known (71−11, 71, s)-Nets in Base 32

Best Known (71−11, 71, s)-Nets in Base 32

(71−11, 71, 2203066)-Net over F₃₂ — Constructive and digital

Digital (60, 71, 2203066)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (15, 20, 525346)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32²⁰, 525346, F₃₂, 6, 5) (dual of [(525346, 6), 3152056, 6]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(32²⁰, 525347, F₃₂, 2, 5) (dual of [(525347, 2), 1050674, 6]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(32³, 1057, F₃₂, 2, 2) (dual of [(1057, 2), 2111, 3]-NRT-code), using
        appending kth column [i] based on linear OA(32³, 1057, F₃₂, 2) (dual of [1057, 1054, 3]-code), using
        Hamming code H(3,32) [i]
        linear OOA(32¹⁷, 524290, F₃₂, 2, 5) (dual of [(524290, 2), 1048563, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(32¹⁷, 1048580, F₃₂, 5) (dual of [1048580, 1048563, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(32¹⁷, 1048576, F₃₂, 5) (dual of [1048576, 1048559, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(32¹³, 1048576, F₃₂, 4) (dual of [1048576, 1048563, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 32⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(32⁰, 4, F₃₂, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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 (40, 51, 1677720)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32⁵¹, 1677720, F₃₂, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
    - OOA 5-folding and stacking with additional row [i] based on linear OA(32⁵¹, 8388601, F₃₂, 11) (dual of [8388601, 8388550, 12]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁵¹, large, F₃₂, 11) (dual of [large, large−51, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

(71−11, 71, 3355440)-Net in Base 32 — Constructive

(60, 71, 3355440)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (16, 21, 8355840)-net in base 32, using
  - base change [i] based on (10, 15, 8355840)-net in base 128, using
    - net defined by OOA [i] based on OOA(128¹⁵, 8355840, S₁₂₈, 5, 5), using
      - appending kth column [i] based on OOA(128¹⁵, 8355840, S₁₂₈, 4, 5), using
        discarding parts of the base [i] based on linear OOA(256¹³, 8355840, F₂₅₆, 4, 5) (dual of [(8355840, 4), 33423347, 6]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 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, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 4, 0) (dual of [(32640, 4), 130560, 1]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 4, 1) (dual of [(32640, 4), 130559, 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, 32640, F₂₅₆, 4, 1) (dual of [(32640, 4), 130559, 2]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 4, 1) (dual of [(32640, 4), 130559, 2]-NRT-code) (see above)
        linear OOA(256³, 32640, F₂₅₆, 4, 2) (dual of [(32640, 4), 130557, 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(256⁷, 32640, F₂₅₆, 4, 5) (dual of [(32640, 4), 130553, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(256⁷, 65281, F₂₅₆, 5) (dual of [65281, 65274, 6]-code), using
        a code by Danev and Olsson [i]
2. (39, 50, 1677720)-net in base 32, using
  - net defined by OOA [i] based on OOA(32⁵⁰, 1677720, S₃₂, 11, 11), using
    - OOA 5-folding and stacking with additional row [i] based on OA(32⁵⁰, 8388601, S₃₂, 11), using
      - discarding factors based on OA(32⁵⁰, large, S₃₂, 11), using
        discarding parts of the base [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

(71−11, 71, large)-Net over F₃₂ — Digital

Digital (60, 71, large)-net over F₃₂, using

5 times m-reduction [i] based on digital (60, 76, large)-net over F₃₂, using
- Gilbertâ€“VarÅ¡amov bound [i]

(71−11, 71, large)-Net in Base 32 — Upper bound on s

There is no (60, 71, large)-net in base 32, because

9 times m-reduction [i] would yield (60, 62, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]

Best Known (71−11, 71, s)-Nets in Base 32

(71−11, 71, 2203066)-Net over F32 — Constructive and digital

(71−11, 71, 3355440)-Net in Base 32 — Constructive

(71−11, 71, large)-Net over F32 — Digital

(71−11, 71, large)-Net in Base 32 — Upper bound on s

(71−11, 71, 2203066)-Net over F₃₂ — Constructive and digital

(71−11, 71, large)-Net over F₃₂ — Digital