MinT - Best Known (69, 69+9, s)-Nets in Base 3

Best Known (69, 69+9, s)-Nets in Base 3

Digital (69, 78, 398580)-net over F₃, using

net defined by OOA [i] based on linear OOA(3⁷⁸, 398580, F₃, 9, 9) (dual of [(398580, 9), 3587142, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3⁷⁸, 1594321, F₃, 9) (dual of [1594321, 1594243, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷⁸, 1594322, F₃, 9) (dual of [1594322, 1594244, 10]-code), using
    - 1 times truncation [i] based on linear OA(3⁷⁹, 1594323, F₃, 10) (dual of [1594323, 1594244, 11]-code), using
      - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Digital (69, 78, 797161)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3⁷⁸, 797161, F₃, 2, 9) (dual of [(797161, 2), 1594244, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁷⁸, 1594322, F₃, 9) (dual of [1594322, 1594244, 10]-code), using
  - 1 times truncation [i] based on linear OA(3⁷⁹, 1594323, F₃, 10) (dual of [1594323, 1594244, 11]-code), using
    - an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

There is no (69, 78, large)-net in base 3, because