MinT - Best Known (45, 53, s)-Nets in Base 32

Best Known (45, 53, s)-Nets in Base 32

(45, 53, 4194300)-Net over F₃₂ — Constructive and digital

Digital (45, 53, 4194300)-net over F₃₂, using

32¹ times duplication [i] based on digital (44, 52, 4194300)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁵², 4194300, F₃₂, 10, 8) (dual of [(4194300, 10), 41942948, 9]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(32⁵², 8388601, F₃₂, 2, 8) (dual of [(8388601, 2), 16777150, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(32⁵², 8388602, F₃₂, 2, 8) (dual of [(8388602, 2), 16777152, 9]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(32¹⁶, 4194301, F₃₂, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
        OOA 2-folding [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]
        linear OOA(32³⁶, 4194301, F₃₂, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
        OOA 2-folding [i] based on linear OA(32³⁶, 8388602, F₃₂, 8) (dual of [8388602, 8388566, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(32³⁶, large, F₃₂, 8) (dual of [large, large−36, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

(45, 53, 4194301)-Net in Base 32 — Constructive

(45, 53, 4194301)-net in base 32, using

32¹ times duplication [i] based on (44, 52, 4194301)-net in base 32, using
- net defined by OOA [i] based on OOA(32⁵², 4194301, S₃₂, 10, 8), using
  - OOA 2-folding and stacking with additional row [i] based on OOA(32⁵², large, S₃₂, 2, 8), using
    - discarding parts of the base [i] based on linear OOA(256³², large, F₂₅₆, 2, 8), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 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, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256⁰, 32769, F₂₅₆, 2, 0) (dual of [(32769, 2), 65538, 1]-NRT-code) (see above)
        linear OOA(256¹, 32769, F₂₅₆, 2, 1) (dual of [(32769, 2), 65537, 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, 32769, F₂₅₆, 2, 1) (dual of [(32769, 2), 65537, 2]-NRT-code) (see above)
        linear OOA(256¹, 32769, F₂₅₆, 2, 1) (dual of [(32769, 2), 65537, 2]-NRT-code) (see above)
        linear OOA(256¹, 32769, F₂₅₆, 2, 1) (dual of [(32769, 2), 65537, 2]-NRT-code) (see above)
        linear OOA(256³, 32769, F₂₅₆, 2, 2) (dual of [(32769, 2), 65535, 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(256³, 32769, F₂₅₆, 2, 2) (dual of [(32769, 2), 65535, 3]-NRT-code) (see above)
        linear OOA(256⁷, 32769, F₂₅₆, 2, 4) (dual of [(32769, 2), 65531, 5]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256⁷, 65538, F₂₅₆, 4) (dual of [65538, 65531, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(256⁷, 65536, F₂₅₆, 4) (dual of [65536, 65529, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(256⁵, 65536, F₂₅₆, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
        linear OOA(256¹⁵, 32769, F₂₅₆, 2, 8) (dual of [(32769, 2), 65523, 9]-NRT-code), using
        OOA 2-folding [i] based on linear OA(256¹⁵, 65538, F₂₅₆, 8) (dual of [65538, 65523, 9]-code), using
        constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [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(256¹³, 65536, F₂₅₆, 7) (dual of [65536, 65523, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code) (see above)

(45, 53, large)-Net over F₃₂ — Digital

Digital (45, 53, large)-net over F₃₂, using

t-expansion [i] based on digital (44, 53, large)-net over F₃₂, using
- 3 times m-reduction [i] based on digital (44, 56, large)-net over F₃₂, using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(32⁵⁶, large, F₃₂, 12) (dual of [large, large−56, 13]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

(45, 53, large)-Net in Base 32 — Upper bound on s

There is no (45, 53, large)-net in base 32, because

6 times m-reduction [i] would yield (45, 47, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]

Best Known (45, 53, s)-Nets in Base 32

(45, 53, 4194300)-Net over F32 — Constructive and digital

(45, 53, 4194301)-Net in Base 32 — Constructive

(45, 53, large)-Net over F32 — Digital

(45, 53, large)-Net in Base 32 — Upper bound on s

(45, 53, 4194300)-Net over F₃₂ — Constructive and digital

(45, 53, large)-Net over F₃₂ — Digital