MinT - Best Known (240−36, 240, s)-Nets in Base 3

Best Known (240−36, 240, s)-Nets in Base 3

Digital (204, 240, 3280)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²⁴⁰, 3280, F₃, 36, 36) (dual of [(3280, 36), 117840, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(3²⁴⁰, 59040, F₃, 36) (dual of [59040, 58800, 37]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴⁰, 59049, F₃, 36) (dual of [59049, 58809, 37]-code), using
    - 1 times truncation [i] based on linear OA(3²⁴¹, 59050, F₃, 37) (dual of [59050, 58809, 38]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]

Digital (204, 240, 19683)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²⁴⁰, 19683, F₃, 3, 36) (dual of [(19683, 3), 58809, 37]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²⁴⁰, 59049, F₃, 36) (dual of [59049, 58809, 37]-code), using
  - 1 times truncation [i] based on linear OA(3²⁴¹, 59050, F₃, 37) (dual of [59050, 58809, 38]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]

There is no (204, 240, large)-net in base 3, because

34 times m-reduction [i] would yield (204, 206, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]