MinT - Best Known (175, 175+21, s)-Nets in Base 3

Best Known (175, 175+21, s)-Nets in Base 3

Digital (175, 196, 478296)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁹⁶, 478296, F₃, 21, 21) (dual of [(478296, 21), 10044020, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3¹⁹⁶, 4782961, F₃, 21) (dual of [4782961, 4782765, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁹⁶, 4782968, F₃, 21) (dual of [4782968, 4782772, 22]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁹⁷, 4782969, F₃, 22) (dual of [4782969, 4782772, 23]-code), using
      - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Digital (175, 196, 1195742)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁹⁶, 1195742, F₃, 4, 21) (dual of [(1195742, 4), 4782772, 22]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3¹⁹⁶, 4782968, F₃, 21) (dual of [4782968, 4782772, 22]-code), using
  - 1 times truncation [i] based on linear OA(3¹⁹⁷, 4782969, F₃, 22) (dual of [4782969, 4782772, 23]-code), using
    - an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

There is no (175, 196, large)-net in base 3, because

19 times m-reduction [i] would yield (175, 177, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]