MinT - Best Known (112−12, 112, s)-Nets in Base 3

Best Known (112−12, 112, s)-Nets in Base 3

Digital (100, 112, 797161)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹¹², 797161, F₃, 12, 12) (dual of [(797161, 12), 9565820, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3¹¹², 4782966, F₃, 12) (dual of [4782966, 4782854, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹¹², 4782969, F₃, 12) (dual of [4782969, 4782857, 13]-code), using
    - 1 times truncation [i] based on linear OA(3¹¹³, 4782970, F₃, 13) (dual of [4782970, 4782857, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (100, 112, 1594323)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹¹², 1594323, F₃, 3, 12) (dual of [(1594323, 3), 4782857, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹¹², 4782969, F₃, 12) (dual of [4782969, 4782857, 13]-code), using
  - 1 times truncation [i] based on linear OA(3¹¹³, 4782970, F₃, 13) (dual of [4782970, 4782857, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (100, 112, large)-net in base 3, because

10 times m-reduction [i] would yield (100, 102, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]