MinT - Best Known (182−21, 182, s)-Nets in Base 3

Best Known (182−21, 182, s)-Nets in Base 3

Digital (161, 182, 159432)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁸², 159432, F₃, 21, 21) (dual of [(159432, 21), 3347890, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3¹⁸², 1594321, F₃, 21) (dual of [1594321, 1594139, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸², 1594322, F₃, 21) (dual of [1594322, 1594140, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁸³, 1594323, F₃, 22) (dual of [1594323, 1594140, 23]-code), using
      - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Digital (161, 182, 398580)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁸², 398580, F₃, 4, 21) (dual of [(398580, 4), 1594138, 22]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁸², 1594320, F₃, 21) (dual of [1594320, 1594138, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁸², 1594322, F₃, 21) (dual of [1594322, 1594140, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁸³, 1594323, F₃, 22) (dual of [1594323, 1594140, 23]-code), using
      - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

There is no (161, 182, large)-net in base 3, because

19 times m-reduction [i] would yield (161, 163, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]