MinT - Best Known (19−4, 19, s)-Nets in Base 32

Best Known (19−4, 19, s)-Nets in Base 32

(19−4, 19, 4195358)-Net over F₃₂ — Constructive and digital

Digital (15, 19, 4195358)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 3, 1057)-net over F₃₂, using
  - kÂ =Â 2 construction [i]
2. digital (12, 16, 4194301)-net over F₃₂, using
  - net defined by OOA [i] based on linear OOA(32¹⁶, 4194301, F₃₂, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(32¹⁶, 8388602, F₃₂, 4) (dual of [8388602, 8388586, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(32¹⁶, large, F₃₂, 4) (dual of [large, large−16, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

(19−4, 19, 8355840)-Net in Base 32 — Constructive

(15, 19, 8355840)-net in base 32, using

32¹ times duplication [i] based on (14, 18, 8355840)-net in base 32, using
- base change [i] based on (11, 15, 8355840)-net in base 64, using
  - net defined by OOA [i] based on OOA(64¹⁵, 8355840, S₆₄, 4, 4), using
    - appending kth column [i] based on OOA(64¹⁵, 8355840, S₆₄, 3, 4), using
      - discarding parts of the base [i] based on linear OOA(256¹¹, 8355840, F₂₅₆, 3, 4) (dual of [(8355840, 3), 25067509, 5]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 3, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32640, F₂₅₆, 3, 0) (dual of [(32640, 3), 97920, 1]-NRT-code) (see above)
        linear OOA(256¹, 32640, F₂₅₆, 3, 1) (dual of [(32640, 3), 97919, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 3, 1) with arbitrarily large s, using
        appending 2 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, 3, 1) (dual of [(32640, 3), 97919, 2]-NRT-code) (see above)
        linear OOA(256³, 32640, F₂₅₆, 3, 2) (dual of [(32640, 3), 97917, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256³, 65793, F₂₅₆, 3, 2) (dual of [(65793, 3), 197376, 3]-NRT-code), using
        appending 1 arbitrary column [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(256⁶, 32640, F₂₅₆, 3, 4) (dual of [(32640, 3), 97914, 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]

(19−4, 19, large)-Net over F₃₂ — Digital

Digital (15, 19, large)-net over F₃₂, using

32³ times duplication [i] based on digital (12, 16, large)-net over F₃₂, using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(32¹⁶, large, F₃₂, 4) (dual of [large, large−16, 5]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

(19−4, 19, large)-Net in Base 32 — Upper bound on s

There is no (15, 19, large)-net in base 32, because

2 times m-reduction [i] would yield (15, 17, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]

Best Known (19−4, 19, s)-Nets in Base 32

(19−4, 19, 4195358)-Net over F32 — Constructive and digital

(19−4, 19, 8355840)-Net in Base 32 — Constructive

(19−4, 19, large)-Net over F32 — Digital

(19−4, 19, large)-Net in Base 32 — Upper bound on s

(19−4, 19, 4195358)-Net over F₃₂ — Constructive and digital

(19−4, 19, large)-Net over F₃₂ — Digital