MinT - Best Known (70, 78, s)-Nets in Base 3

Best Known (70, 78, s)-Nets in Base 3

Digital (70, 78, 2097150)-net over F₃, using

3² times duplication [i] based on digital (68, 76, 2097150)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁷⁶, 2097150, F₃, 8, 8) (dual of [(2097150, 8), 16777124, 9]-NRT-code), using
  - OA 4-folding and stacking [i] based on linear OA(3⁷⁶, 8388600, F₃, 8) (dual of [8388600, 8388524, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Digital (70, 78, 4194302)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁷⁸, 4194302, F₃, 2, 8) (dual of [(4194302, 2), 8388526, 9]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3⁷⁶, 4194301, F₃, 2, 8) (dual of [(4194301, 2), 8388526, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁷⁶, 8388602, F₃, 8) (dual of [8388602, 8388526, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

There is no (70, 78, large)-net in base 3, because