MinT - Best Known (217−28, 217, s)-Nets in Base 3

Best Known (217−28, 217, s)-Nets in Base 3

Digital (189, 217, 37960)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²¹⁷, 37960, F₃, 28, 28) (dual of [(37960, 28), 1062663, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3²¹⁷, 531440, F₃, 28) (dual of [531440, 531223, 29]-code), using
  - discarding factors / shortening the dual code 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, 217, 123568)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²¹⁷, 123568, F₃, 4, 28) (dual of [(123568, 4), 494055, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²¹⁷, 132860, F₃, 4, 28) (dual of [(132860, 4), 531223, 29]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3²¹⁷, 531440, F₃, 28) (dual of [531440, 531223, 29]-code), using
    - discarding factors / shortening the dual code 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, 217, large)-net in base 3, because

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