MinT - Best Known (21, 21+6, s)-Nets in Base 3

Best Known (21, 21+6, s)-Nets in Base 3

Digital (21, 27, 364)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²⁷, 364, F₃, 6, 6) (dual of [(364, 6), 2157, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(3²⁷, 364, F₃, 5, 6) (dual of [(364, 5), 1793, 7]-NRT-code), using
  - OA 3-folding and stacking [i] based on linear OA(3²⁷, 1092, F₃, 6) (dual of [1092, 1065, 7]-code), using
    - 1 times truncation [i] based on linear OA(3²⁸, 1093, F₃, 7) (dual of [1093, 1065, 8]-code), using
      - the BCH-code C(I) with length 1093Â | 3⁷âˆ’1, defining interval IÂ =Â {−3,−1,1,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

Digital (21, 27, 1092)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²⁷, 1092, F₃, 6, 6) (dual of [(1092, 6), 6525, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(3²⁷, 1092, F₃, 5, 6) (dual of [(1092, 5), 5433, 7]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁷, 1092, F₃, 6) (dual of [1092, 1065, 7]-code), using
    - 1 times truncation [i] based on linear OA(3²⁸, 1093, F₃, 7) (dual of [1093, 1065, 8]-code), using
      - the BCH-code C(I) with length 1093Â | 3⁷âˆ’1, defining interval IÂ =Â {−3,−1,1,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]

There is no (21, 27, 17881)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 625990 908987 > 3²⁷ [i]