MinT - Best Known (189, 189+27, s)-Nets in Base 3

Best Known (189, 189+27, s)-Nets in Base 3

Digital (189, 216, 40879)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²¹⁶, 40879, F₃, 27, 27) (dual of [(40879, 27), 1103517, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3²¹⁶, 531428, F₃, 27) (dual of [531428, 531212, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹⁶, 531440, F₃, 27) (dual of [531440, 531224, 28]-code), using
    - 1 times truncation [i] based on linear OA(3²¹⁷, 531441, F₃, 28) (dual of [531441, 531224, 29]-code), using
      - an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]

Digital (189, 216, 132860)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²¹⁶, 132860, F₃, 4, 27) (dual of [(132860, 4), 531224, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3²¹⁶, 531440, F₃, 27) (dual of [531440, 531224, 28]-code), using
  - 1 times truncation [i] based on linear OA(3²¹⁷, 531441, F₃, 28) (dual of [531441, 531224, 29]-code), using
    - an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]

There is no (189, 216, large)-net in base 3, because

25 times m-reduction [i] would yield (189, 191, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]