MinT - Best Known (176−24, 176, s)-Nets in Base 3

Best Known (176−24, 176, s)-Nets in Base 3

Digital (152, 176, 14762)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁷⁶, 14762, F₃, 24, 24) (dual of [(14762, 24), 354112, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3¹⁷⁶, 177144, F₃, 24) (dual of [177144, 176968, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁷⁶, 177147, F₃, 24) (dual of [177147, 176971, 25]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁷⁷, 177148, F₃, 25) (dual of [177148, 176971, 26]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

Digital (152, 176, 55619)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁷⁶, 55619, F₃, 3, 24) (dual of [(55619, 3), 166681, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁷⁶, 59049, F₃, 3, 24) (dual of [(59049, 3), 176971, 25]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁷⁶, 177147, F₃, 24) (dual of [177147, 176971, 25]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁷⁷, 177148, F₃, 25) (dual of [177148, 176971, 26]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]

There is no (152, 176, large)-net in base 3, because

22 times m-reduction [i] would yield (152, 154, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]