MinT - Best Known (220−30, 220, s)-Nets in Base 3

Best Known (220−30, 220, s)-Nets in Base 3

Digital (190, 220, 11809)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²²⁰, 11809, F₃, 30, 30) (dual of [(11809, 30), 354050, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3²²⁰, 177135, F₃, 30) (dual of [177135, 176915, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²⁰, 177147, F₃, 30) (dual of [177147, 176927, 31]-code), using
    - 1 times truncation [i] based on linear OA(3²²¹, 177148, F₃, 31) (dual of [177148, 176927, 32]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]

Digital (190, 220, 50603)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²²⁰, 50603, F₃, 3, 30) (dual of [(50603, 3), 151589, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²²⁰, 59049, F₃, 3, 30) (dual of [(59049, 3), 176927, 31]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²²⁰, 177147, F₃, 30) (dual of [177147, 176927, 31]-code), using
    - 1 times truncation [i] based on linear OA(3²²¹, 177148, F₃, 31) (dual of [177148, 176927, 32]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]

There is no (190, 220, large)-net in base 3, because

28 times m-reduction [i] would yield (190, 192, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]