MinT - Best Known (119, 119+21, s)-Nets in Base 3

Best Known (119, 119+21, s)-Nets in Base 3

Digital (119, 140, 5904)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁴⁰, 5904, F₃, 21, 21) (dual of [(5904, 21), 123844, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3¹⁴⁰, 59041, F₃, 21) (dual of [59041, 58901, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁴⁰, 59048, F₃, 21) (dual of [59048, 58908, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using
      - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Digital (119, 140, 19682)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁴⁰, 19682, F₃, 3, 21) (dual of [(19682, 3), 58906, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁴⁰, 59046, F₃, 21) (dual of [59046, 58906, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁴⁰, 59048, F₃, 21) (dual of [59048, 58908, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using
      - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

There is no (119, 140, large)-net in base 3, because

19 times m-reduction [i] would yield (119, 121, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]