MinT - Best Known (210, 210+30, s)-Nets in Base 3

Best Known (210, 210+30, s)-Nets in Base 3

Digital (210, 240, 35429)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²⁴⁰, 35429, F₃, 30, 30) (dual of [(35429, 30), 1062630, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3²⁴⁰, 531435, F₃, 30) (dual of [531435, 531195, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴⁰, 531441, F₃, 30) (dual of [531441, 531201, 31]-code), using
    - 1 times truncation [i] based on linear OA(3²⁴¹, 531442, F₃, 31) (dual of [531442, 531201, 32]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]

Digital (210, 240, 132860)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²⁴⁰, 132860, F₃, 4, 30) (dual of [(132860, 4), 531200, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3²⁴⁰, 531440, F₃, 30) (dual of [531440, 531200, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴⁰, 531441, F₃, 30) (dual of [531441, 531201, 31]-code), using
    - 1 times truncation [i] based on linear OA(3²⁴¹, 531442, F₃, 31) (dual of [531442, 531201, 32]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]

There is no (210, 240, large)-net in base 3, because

28 times m-reduction [i] would yield (210, 212, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]