MinT - Best Known (241−25, 241, s)-Nets in Base 3

Best Known (241−25, 241, s)-Nets in Base 3

Digital (216, 241, 699050)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²⁴¹, 699050, F₃, 25, 25) (dual of [(699050, 25), 17476009, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3²⁴¹, 8388601, F₃, 25) (dual of [8388601, 8388360, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴¹, large, F₃, 25) (dual of [large, large−241, 26]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Digital (216, 241, 1871366)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²⁴¹, 1871366, F₃, 4, 25) (dual of [(1871366, 4), 7485223, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²⁴¹, 2097150, F₃, 4, 25) (dual of [(2097150, 4), 8388359, 26]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3²⁴¹, 8388600, F₃, 25) (dual of [8388600, 8388359, 26]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁴¹, large, F₃, 25) (dual of [large, large−241, 26]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

There is no (216, 241, large)-net in base 3, because

23 times m-reduction [i] would yield (216, 218, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]