MinT - Best Known (133, 133+21, s)-Nets in Base 3

Best Known (133, 133+21, s)-Nets in Base 3

Digital (133, 154, 17714)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁵⁴, 17714, F₃, 21, 21) (dual of [(17714, 21), 371840, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3¹⁵⁴, 177141, F₃, 21) (dual of [177141, 176987, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁴, 177146, F₃, 21) (dual of [177146, 176992, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁵⁵, 177147, F₃, 22) (dual of [177147, 176992, 23]-code), using
      - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Digital (133, 154, 59048)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁵⁴, 59048, F₃, 3, 21) (dual of [(59048, 3), 176990, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁵⁴, 177144, F₃, 21) (dual of [177144, 176990, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁴, 177146, F₃, 21) (dual of [177146, 176992, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁵⁵, 177147, F₃, 22) (dual of [177147, 176992, 23]-code), using
      - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

There is no (133, 154, large)-net in base 3, because

19 times m-reduction [i] would yield (133, 135, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]